As Catholics we profess to believe in:
the Holy Spirit, the Holy Catholic Church, the communion of saints, the resurrection of the body and life everlasting.
The Catechism of the Catholic Church states that
“On no point does the Christian faith encounter more opposition than on the resurrection of the body.” It is very commonly accepted that the life of the human person continues in a spiritual fashion after death. But how can we believe that this body, so clearly mortal, could rise to everlasting life? (CCC 994)
How can we believe it? Because
“The flesh is the hinge of salvation” (Tertullian, De res. 8, 2:PL 2, 852). We believe in God who is creator of the flesh; we believe in the Word made flesh in order to redeem the flesh; we believe in the resurrection of the flesh, the fulfillment of both the creation and the redemption of the flesh. (CCC 1015)
The body is not a prison cell for the soul. Death is not a matter of “freeing” our souls from the confines of our wretched bodies. In fact, in the beginning, God saw the union of Adam’s body and soul and declared it to be “very good.” This union of body and soul untouched by sin is what Christ came and will come again to restore us to, only now in a more glorified way.
…all who are in the tombs will hear his voice and will come out, those who have done good deeds to the resurrection of life, but those who have done wicked deeds to the resurrection of condemnation. (Jn. 5:28-29)
…how can some among you say there is no resurrection of the dead? If there is no resurrection of the dead, then neither has Christ been raised. (1 Corinth 15:12-13)
If the Spirit of the one who raised Jesus from the dead dwells in you, the one who raised Christ from the dead will give life to your mortal bodies also, through his Spirit that dwells in you. (Romans 8:11)
But our citizenship is in heaven, and from it we also await a savior, the Lord Jesus Christ. He will change our lowly body to conform with his glorified body by the power that enables him also to bring all things into subjection to himself. (Phil. 3:21)
Behold, I tell you a mystery. We shall not all fall asleep, but we will all be changed, in an instant, in the blink of an eye, at the last trumpet. For the trumpet will sound, the dead will be raised incorruptible, and we shall be changed. (1 Corinth 15:51-52)
Christopher West has a good article on The Resurrection of Our Bodies:
During this Easter season it is fitting to reflect on the resurrection not just of Jesus’ body, but of our own bodies at the end of time. Many people have an erroneous “super-spiritual” view of eternal life. Such people tend to see the body as a shell that they’re anxious to get rid of, as if death were the moment in which our souls were finally “liberated” from the “prison” of our bodies…
We often speak of the “souls” in heaven. When we buried my grandmother, I saw her body go in the ground and I’m confident that her soul is now enjoying some form of union with God. But the souls currently in heaven (“currently,” of course, is a time-bound word which doesn’t even apply to heaven) remain in an “inhuman” state until the resurrection of their bodies. It can’t be any other way for us as human beings. Since God created us as a union of body and soul, the separation of the two at death is entirely “unnatural.” Indeed, it’s a cosmic tragedy.
Our bodies will certainly be different in their resurrected state. Recall that the disciples didn’t readily recognize Jesus after the resurrection (see Lk 24:15-16). But at the end of time, we will certainly have our bodies, as does Jesus.