I've always been taught that "the" is for when there's a single obvious instance you're talking about. There are many policemen and women, but if I say "the police" there's only really one likely candidate which I could be talking about.

"A man" is just some guy. If I say "The man" there's a specific guy I'm talking about and I expect you to know which one.

Did you know dutch has two words for "the"? One is generally for big or important things and the other for small or unimportant things. I'm sure people trying to learn Dutch love figuring out which you use when.