That means you'd expect it to be very common. Not having a lot of donuts would be weird. (Now there's a maxim to live by!)
Yes, it's extremely handwavy, and there are probably explanations that are much better and more detailed. Sorry. Best I have.
[1] I lie. It's a compact orientable 2-manifold, not a 2D surface. For laymen's terms, I hope the math folks will let me get away with "surface" though.
The antipodal points Pac-Man and so while a 360 degree rotation is considered 'invariant' that only holds for rigid objects with no connections.
Rolling up a hose, twirling a baton, or the belt trick shows that 720 is the real invariant rotation.
Merge and Delete those two points at infinity and you get a donut.
Imagine a clock laying on a table, and then placing clocks at each number which are rotated that number of steps. (Equivalently, so the number on the new clock matches the original clock at that spot.) If you trace where the numbers are on these clocks, you get bands that twist around the torus. This shape [0].
So we have:
1. Product of two circles.
2. A simple 2D shape with a hole.
3. Addition.
…all mixed up in one shape. So it shows up a lot of places.
[0] - https://d2r55xnwy6nx47.cloudfront.net/uploads/2020/05/Knot-S...