Receiving Christ's life as our own, the life He laid down for us. That doesn't guarantee that we will live long lives. Nor does it say that we will be necessarily wealthy or healthy. Abundant life doesn't consist in the abundance of possessions. Peter reminds us that the call to live in Christ is a call to share in His sufferings.
Abundant life means eternal life.
Life overflowing with life. So much life it can never be expended or exhausted, no matter what happens to us in this life. Jesus came to give us eternal life, his life, a life that conquered death and the grave. Jesus died to destroy the death that threatens our lives. He bore our sins in his own body on the tree.