I have a toilet tank that looks like every other tank I've ever seen, but in the center, there is a "box" that separates the 1/3 of the water from the rest.

Effectively, when I flush, it only uses 1/3 of the tank's water.

Does anyone have any idea what this is and why it's there?

What you have is a Low Flush toilet. This set up was used some years back when new low flush regulation came into effect and some toilet manufacturers couldn't redesign their toilets in time to comply . So instead, they designed what you have inside your toilet tank. That "box" actually displaces only about 1.6 gln of water per flush instead of entire tank. I am not sure, whether they still use this design today, but have not seen one in some time.

Thanks. Can it be removed?

Yes, it can be removed with some effort, though. Or you can cut it down so more water is released to the bowl. However, by removing it, you will create non-Low Flush toilet.

Thanks. I am *trying* to make it non-low flush. It just doesn't work very well, and often takes two or three flushes and a plunger.

I'm hoping more water will remedy the problem until I replace the entire tank with a more modern low-flow.

Sure, the easiest way is to take scissors a cut into wall of the box removing wall as much as you can. It doesn't have to be removed entirely for your toilet to become 3.5 gln a flush toilet again.