Q1: Why does Jesus appear after his Resurrection?
Q2: How many times did Jesus appear to people? Q3: How did he resurrect and appear as he did? Q4: What did he do when he appeared?
Q5: Why's it matter?
Question 1: Why does Jesus appear after his Resurrection?
Answer 1: St. John's Gospel tells us that Jesus did many signs and wonders so that we might believe, not so that we can have a historical account, and having found that, might believe. Without the Resurrection we would still be dead in our sins, since it would be evidence that no man had defeated Death, the great Curse of Man's Fall. Jesus' Resurrection is a sign that he has tasted death, plundered Hell, and defeated Death. If the effect is gone, then so too must be the cause; in logic we call this a modus tollens. Thus Sin is dead through Jesus Christ. His appearances are to give us surety and confidence that following him is The Way, the Truth, and The Life
Question 2: How many times did he appear?
Answer: We're not quite sure. St. John also tells us he appeared and did many signs and wonders not recording in his Gospel. And St. Paul tells us of an appearance in his First Epistle to the Corinthians that didn't appear in any of the Four Gospels. We shall need The Tradition as well as Scriptures to know, but "creating an exhaustive list" is not, nor ever was, the purpose of these texts. It would seem somewhere between ten or twelve appearances are recorded, depending on Scriptural arguments and cross references. For those appearances see Question #4.
Question 3: How did resurrect and appear as he did?
Jesus is God. God is the Lord of all things and the entire universe, which includes space and time. Thus Christ is the Lord of all time and space. His divine nature and human soul, being cleft from his body, descended into hell. By the power of the Divine Substance, which is Life-Itself, he resurrected and returned his human soul to his body. By the unity of the human nature and divine substance in one Person, Jesus, the human returned to life. This fulfills Ezekiel's prophetic vision of dry bones regathering tendons, muscles, skin, and then coming back to life. It also fulfills Job's Hope that "from my flesh I shall see God." I.E. We see Jesus personally, with our eyeballs, like you look at a friend now.
Jesus appears and disappears from a locked room. If there's a way to teleport or pass through walls while maintaining corporal existence, Jesus seems to do it here. He appears yet eats food; it doesn't pass through him like a ghost.
Jesus did not rise from the dead so we could live as bubbly spirits in an ethereal heaven, but he rose that we might rise again one day with our bodies and live out our existence on a perfected cosmos. We don't become angels with harps or exist as ideas, we resurrect and thus continue to be fully human, soul and body. This is the difference between Cartesian Christianity that sees the body as a prison and the Catholic Faith that sees the body as good and essential to our identity. We do not 'have' bodies, we 'are' bodies, rational ones at that. This is why if I stab you with a pen, you do not say, "Ow, you hurt my property," but "Ow, you stabbed me." This means how you treat yourself physically, emotionally, are expressions of whether or not you think your body is worth resurrecting. Life then is not about "self-expression," as if the "Self" is the ghost inside my flesh suit, no, it is about you cultivating embodied ways of life here and now that are full expressions of the resurrected life to come. The Earth should reflect our Hope in the way we form our lives now. We are not "waiting for heaven," we're practicing for the New Heavens and the New Earth now.
Question 4: What did he do when he appeared?
1. To Mary Magdalene, the whom he cast out seven demons. She thought he was a Gardener, signifying the Second Adam and the Second Garden of Eden, and Christ's blood from the cross as the fruit of the Second Tree of Life.
2. Mary Magdalene, Mary Clopas, Mary mother of James and Joanna. He tells them to tell The Apostles to come to a mountain in Galilee.
3. Simon Peter. It is Simon who will take over the office Christ played as over the Apostles. Thus the First Pope, Vicar of Christ, is given a special greeting.
4. The two disciples on the Emmaus Way. Here Jesus is unknown by the two friends, he explicates the Scriptures and where you see Jesus throughout all the Old Testament (e.g. the Rock in the Wilderness in Exodus and Numbers, the Word speaking in Genesis, the Word of the Lord that spoke through all the prophets, his foreshadows through people like Melchizedek, David, etc.) It's not until they reach their destination and receive the eucharist that they see and understand the man is Jesus resurrected. We must take note it wasn't programs or camps or Sunday school or feelings or experiences that allowed these Christians to know Jesus, it was the eucharist alone. This opened their eyes to understand everything else.
5. To ten Apostles -- Thomas the Twin was absent and Judas was dead. This is the Easter Sunday Evening and they are still in Jerusalem, the capitol city of Israel. He appears to them in The Upper Room, the same room that Jesus did The Passover with them on Maundy Thursday. Again he reiterates to his new priests, The Apostles, that they must (1) take (2) bless (3) break & (4) give. This can be seen as the Master reiterating training for his disciples and how they must continue his Church. There are many appearances on Easter Day.
The Easter Octave, 8 days after Easter Sunday, being "Divine Mercy Sunday"
6. He appears to the Apostles again, this time Thomas the Twin is there. He places his finger in the opening where Jesus was crucified. He believes. Jesus tells us blessed are those who see and do not believe. This all happens a week after he appeared to the other apostles. This is why we read this Gospel at Mass on the Second Week of Easter to this day.
The Third Sunday of Easter
7. Jesus appears to Seven: Peter, Thomas, Nathaniel/Bartholomew, James, John, and two unnamed disciples go fishing at the Sea of Tiberius. Jesus helps them bring in a big haul of 153 large fish, signifying they will soon catch many men at Pentecost. Peter jumps off the boat and swims to shore before the other makes it. Peter goes to the 'beach confessional.' Jesus gives Peter penance by asking him to confess his love for Jesus thrice, since Peter denied him thrice. Jesus asks if Peter loves Jesus more than the other Apostles, and Jesus charges Peter to feed (Teach Doctrine), tend to (Govern as Pastor), and to feed (Sanctify by the Mass) his sheep. Having been reconciled, Jesus celebrates Mass with the breaking of the bread.
8. He appears to 500 disciples. This may be before Galilee or during, but doesn't seem to occur after it. If it is during Galilee it might be before he goes up the Mountain to see The Apostles, which would reflect God telling Moses none of the Israelites are to go up the Mountain but only Moses. Or it might be an echo of Jesus' Homily on the Mount where many disciples were gathered, and here he gives one final homily. If it is at the Mountain then this is the same as #9.
9. Jesus appears to the Apostles on the mountain of Galilee. Remember Jesus told Mary Magdalene to deliver this message on Easter Sunday. Here they meet him like the Israelites gathered around Moses and God on Mount Sinai. Jesus charges them to 'Go forth and baptize all the Gentiles in the name of the Father and of the Son and of the Holy Spirit.' Paul will take him up on this in Acts after his own conversion to The Faith.
10. Jesus appears to James and then to all the Apostles. This could be a reference to #9 at the Mountain or it could be #10 as they approached the table one last time. Or it could be an independent event altogether. This could be James Zebedee, brother to John, in which case it could be this special appearance signals James as the first Apostolic Martyr (he dies by the sword in Acts). Or it could be James the Just, Jesus' cousin, who became a Bishop of Jerusalem.
11. They celebrate The Mass one final time at the table and they know it is the last time with him under the species of Man. Henceforth they shall have to see him under the species of bread and wine with the eyes of Faith, "Blessed are those who do not see and yet believe."
12. Forty Days after Easter Sunday Jesus appears, gives them a blessing, and is taken up by The Holy Spirit appearing in the figure of a cloud. This is his last Resurrection appearance. The Apostles stand stupefied until angels call their attention back down to earth. They're told to get to work. Christ has trained them in the Christian Philosophy, to practice The Faith by keeping to: (1) The Mass (2) The Prayers (3) The Doctrine (4) The Fellowship. They go back to The Upper Room pray for nine days, the first Novena, and on the tenth day The Holy Spirit descends again, this time with tongues of fire. Having already been baptized The Spirit's outpouring Confirms them and they begin their ministry by preaching to their fellow Jews to"Repent, and be baptized."
Question 5: Why's it matter?
The Resurrection flies in the face of Gnostic Christianity, Dualism, and Consumerism. Unfortunately the political categories of "conservative" and "liberal" are not up to the task of facing these three down and living a life consonant with The Resurrection, largely because those political categories are the historical children of these three problems. There's more to be said that and can be done in another article. The short hand answer is to read Acts of the Apostles. During Eastertide this book replaces the Old Testament Lesson in Mass because it shows an embodied way of life that is the practice of The Faith. The Cross without Resurrection or the Early Church is simply Protestantism -- "Jesus did all and now let's go get a Combo #2 and make it back in time for another hour of TV and phone apps at the same time."
If we're wondering whether or not we believe in The Resurrection then we must ask ourselves the question, "If it turns out The Resurrection is false, would I still do the things I currently do? Yes or no? Do my current forms of life make sense without The Resurrection? Yes or no? If the answer to either is Yes, then one's imagination has been captured by a non-Catholic theology. But Christ resurrected having set all captives free. So too then, we ought be. Alleluia! Christ is Risen! The Lord is Risen indeed! Alleluia!