What exactly does "prego" mean?

That is a question all foreigners ask themselves. The most common translation for prego is "You are welcome" or "No problem". However, Italians use it in plenty of different ways. If you want here there is a video that well explain the way Italians use this word.

https://www.youtube.com/watch?v=SOoFAuTms34

This is a twelve year old question you are answering, but I am quite glad you did.
That video presents by far the best explanation I've seen or heard.

I studied italian for a few years in the early nineties and have been to Italy a few times, on very satisfying trips. That video makes me want to refresh my memory of the language I somewhat understood back then. The last time I was there, 1999, I could still make my way alone through different cities with my mediocre italian. People there tend to support those who are trying to learn.

Oh, I finally get it. It's like an American 'whatever', but more polite.

More like the word 'Please' which has many nuances of meaning too.

good analogy!

Your English really sucks. There is absolutely no reason to believe that you are a native speaker of English.

Heh, Kicky knows way more italian than you do.