The Tuck family shares their secret of immortality with Winnie. I suppose their secret contains two parts. First, they are immortal and can't die. Second, the Tucks share the source of their immortality. It is a magic spring that is in the woods near Winnie Foster's house in Treegap.
In Chapter Five, Winnie decides to go into the woods in order to get away from her family for a bit. Winnie arrives at the spring and sees Jesse Tuck drinking from it. She tries to take a drink too, but Jesse won't let her. Eventually, Mae and Miles Tuck show up. They realize what has happened and decide to "kidnap" Winnie. On the way back to the Tuck house, the three Tucks tell Winnie about the spring and their immortality.