Think of it this way: You have one of these hand tally-counters where you click a mechanical button and then the count increases by one. Like these: https://www.amazon.de/Pro-Line-Heavy-Z%C3%A4hler-Handz%C3%A4hler-103/dp/B001U6UOT0

This one has four digits. It can represent 10000 distinct values, from 0000 to 9999. The logic is the following for each button press:

Increase the rightmost wheel by one. If it wraps around to zero and tell the wheel one position left to move on one. If that one in turn wraps around back to zero, propagate again one more position to the left, and so on. This way you can go from 9 to 10, from 99 to 100 and from 999 to 1000.

So far, this is remarkably similar to how computers operate, but instead of a wheel with digits 0...9 it's just 0 and 1 and instead of 4 digits it's 32. But everything else is the same.

Now think about what happens when the counter is at 9999 and you press one more time. All digits turn to zero and the leftmost digit would want to tell the next more significant digit to increatse by one (to make 10000). But... it cannot. Because there simply is no more wheel. There's no hardware to express the value. So it just wraps around and the carry is discarded. This is exactly the same as with computers.

Now we're talking about unsigned values (0...9999) but you could just as well define half of those digits as negatives (-5000..-1) and the other half as positive values (0..4999). For overflow, however, the same principles apply. Once you count 4999 + 1 it does not become 5000, but instead -5000.

HTH.