self learning - What is modular arithmetic?

I always see questions on here that deal with this modular stuff, and I have no idea what any of it means, so I figured I would ask here.

So lets say we have
$$a \equiv b\pmod n$$
The example on wiki is $$38\equiv 14\mod 12$$
This is because 38-14 = 24, which has a factor of 12. Why is it 12 instead of 24, 3, 4? It gives an practical example of a clock. I get that that is a mod 12 (I think) but how do I write that in the notation used above? This is just some self learning in the small spare time I have