Time is a bit of a weird thing, and there are all sorts of theories to describe it. But the simplest is that's just another dimension, at right-angles to all the other three. For reasons unknown, we appear to be moving at a constant speed through spacetime -- the speed of light.

Imagine a large sheet of paper. The length of the paper corresponds to time; all the other dimensions (up/down, left/right, forward/backward) are "collapsed" together and are represented by the width of the paper.

Now think of a little model car that can be steered, but it always travels at a fixed speed, which we'll call "c". When it's going forward along the length of the paper, it's standing still in space (it's not going backward, forward, left, right, up or down) but moving forward in time at the speed "c". But if it changes direction and moves at an angle, although the speed of the car remains constant at "c", it's travelling through time at a slightly slower rate. If you steer it so that it's going at right angles to the length of the paper, it is travelling at "c" in space, but not at all through time. The constant "c" is actually the speed of light, so this is a very simple demonstration of what's called "time dilation", the idea that time slows down for us the faster we move.

Unfortunately, our little model car doesn't have a reverse gear; and for some reason, we can't actually get it to turn around. In our universe, it doesn't seem possible to travel back in time, only forward or (in theory but not actually in practice as long as you have mass) not at all, but never backward. Or so it seems: actually, nobody's 100% sure, but the fact that we're not continually meeting time travellers from the future suggests it might not be possible, or not practicable.

But let's return to the model car moving along the paper at speed "c". Now, where does the paper go?

It doesn't "go" anywere: it just exists, and the car is moving along it. That's it, plain and simple.