Compel means to force or drive someone to do something. Even if you don't like toast, when you visit the toast-eating natives of Shrintakook Island, you'll be compelled to eat it, or they will not trust you.
You don't want to be compelled to go to a classical music concert if you'd rather listen to rap. School officials might be upset if a winter storm compels them to cancel classes, but you'd be okay with that. A compelling mystery forces you to pay attention because you want to find out "whodunit."