Enoch has one of the most peculiar of the peculiar abilities: He can bring things back to life. It's not as easy as touching them and getting them to talk, though—he has to "take the life of one thing and give it to another" (8.71). What this means is that he has to have an animal heart to bring something else back to life. This comes in handy when the group needs to interrogate a murder victim.
He can even give life to inanimate objects. When Jacob first meets him, Enoch is playing with his "homunculi" (8.58) (he really should do that in private). They're little clay creatures he brings to life and torments. If that's not a serial-killer warning sign, we don't know what is.
When Enoch's not bringing the dead to life, or animating his dolls (we're not sure which is creepier), he's a bit of a troublemaker. Enoch stirs up Jacob by telling him about Raid the Village and tricking him into sneaking into a room in Miss Peregrine's, but he ultimately ends up being a reliable member of the team to save Miss Peregrine in the end.