Chronotron is at its heart a conventional puzzle-platformer; your little guy appears on the screen along with his Tardis, and somewhere else on the screen is a "time machine" part you need to retrieve and return to your Tardis. Arrow keys to move (up-arrow to jump), with the occasional crate to pick up and move, buttons to stand or put crates on, and so forth. We've seen this before.
What we haven't seen before, is the "time travel" effect. That is, lots of people have been experimenting with time travel in one form or another in indie games recently, perhaps inspired by Braid, but Chronotron uses the motif in a straight-forward way that works very well in a platform-puzzler context. By returning to your Tardis and pressing the space bar, you hop in, and then reappear--and so does your previous self, who goes off and performs whatever actions you performed the last time you left the Tardis.
Thus, "yourself" is a resource you can use to, say, hold buttons down so your more recent self can get where you want to go. An example is perhaps the best way of explaining: In the level pictured above, the solution is this: self one goes and stands on the left pylon, pressing it down and elevating the other, for 30 seconds or so. Self 2 waits for ten seconds, then joins self 1 on the left pylon, elevating the right pylon further. Self 3 runs to the right pylon, jumps atop it (this is why self 2 waits, to give self 3 enough time). When self 2 jumps on the left pylon, the right is now high enough for self 3 to jump up to the area with the machine part. He can then easily enough return to the Tardis with it.
Chronotron has neither the elaborate and imaginatively detailed exploration of the time mechanics that Braid provides, nor its evocative story; but Chronotron is a simple, satisfying, and enjoyable exploration of the effects of one novel mechanic on a well-established form.