To enlist is to voluntarily join the military. You may have seen television commercials or posters encouraging people to enlist.
There are various ways people end up in the military. Sometimes there's a draft, which selects people whether they want to go or not. Sometimes people enlist, which means they sign up on their own. Enlisting also refers to recruiting or hiring people for some purpose or organization. If you are moving, you might try to enlist your friends to help — good luck with that.