From what I'm seeing, the Apple TV will indeed support sub titles (closed captioning) as long as the original media has it. This means that the show/movie/whatever must have the sub titles as it comes from the distributor. If it does, the new Apple TV will supposedly let you use them.
However, there have been some reports that the sub titles are rendered in a font that's too small to see. That may be an issue that Apple will address with a future software update. Time will tell.
There's also a software product that will do soft sub titles for Apple TV as well as other devices. It's called iSubTitle. Reviews on it sound pretty good.
Of course, keep in mind that since I don't personally use sub titles, this is all based on things I've seen or heard about. I don't have any personal usage experience with these things to share.
Tom (... hope it helps!)