There is no way that I can give you a short answer to a quite complex matter; so why don't you just read here:
http://en.wikipedia.org/wiki/Peer-to-peer
http://en.wikipedia.org/wiki/File_sharing

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"Never Argue With An Idiot. They Will Drag You Down To Their Level, Then Beat You With Experience"

Thanx Iv'e read that but I'm still no wiser.

The thing is, what I'm trying to say is surely if a person uploads songs from me they would still be on their computer, so therefore when I do a search for them they should be in the normal search you would think do you see what I'm trying to say?

That requires those people being online at the time of your search, having not deleted, moved or renamed the file. Only when this is given, those files will show up in your search......

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"Never Argue With An Idiot. They Will Drag You Down To Their Level, Then Beat You With Experience"

You know its strange cause I was chatting to a guy from Italy who just uploaded one of my MP3's and I said to him stay online and keep the file in your shared folder, he replyed I always do anyway, so I thought this is my chance to do a normal search just like as if I was after that song but didn't have it, that sort of search, anyway I typed the artist and name of song and it showed no results of my file, and then I tryed just artist, then just song title, still nothing.

How can this be?