Literally, to poke someone. Typically this is done over an IM client.
Part of the old school emote family (yeah, before lolcats).
Like anything enclosed in asterisks, *poke* is performing the action of poking the person you send it to.
Largely replaced, in modern context, with "/e", "/me" or "/em" (emote) preceding the action.
Bro: Hey Dude, what's up?
<Long period of silence>
Bro: *Poke* Oi! Wake up!
Dude: ouch! Sorry was doing other stuff!