T.S.
My son is 2yrs 7mos and we have been using timeouts since he turned 2. And I can tell you that he knows exactly what they are. We give time-outs for hitting, spitting and jumping on the couch. If he goes to hit me, I will look at him and say, "No hitting. What happens when you hit?" He will respond and say, "Time-out." When we first started the timeout for hitting, he would come up to me, say "time out" and then hit me. He KNEW what it would lead to.
He doesn't like timeouts and will cry/moan when he's in there. Like your daughter, our son does NOT sit still for anything. But, we just tell him that he has to "sit down in time out". If he gets up, the 2 minutes starts over again. We weren't that strict at first since he was new to it, but we evolved into it. He will sit still for them but just this weekend, he started to stand up and laugh when I came over to have him sit down. It's always new and exciting, huh? I just kept going over and sitting him down. All I said was, "Sit down in timeout" while I sat him back down. I must have done it 15 times, but eventually he gave up and sat for the 2 minutes. After ALL of that, he still knew what he did to get in timeout when I asked him.
So yea, they know.
Good luck.
T.
Edited to add: Just this weekend, he threatened a timeout to his "teddy" for jumping on the couch.