The camera is on all the time the screen is tracking your eyes! That uses battery life. One review test clocked the feature using over an hours battery life per cycle!
That's not correct - it doesn't track your eyes all the time.
The way Samsung implemented it in the Galaxy S3 (I assume it's the same for the S4) is that every time your screen is about to time out, the camera checks if you're looking at the screen. If you are, it keeps the screen on until the next time it's about to time out again.
That said, while I think it's a pretty cool feature, it probably makes more sense to just disable screen timeout altogether and lock the device manually.