This might seem like a no-brainer, but Apple allows 5 computers to have access to your paid-for library. So this can apply to your home desktop, laptop, your old clunker you left at your parents, office PC, and maybe a computer or 2 you use when you are at a friend’s house.
That last bit is where iTunes grants some flexibility. It doesn’t know who your friends are. You might have some legal ownership to the computer, and even if you don’t- you still use it and have a right to listen to your library locally when using somebody else’s computer. It’s similar to the circle of friends features (My 5) that cell-phone services offer.
Being able to pool music from your friends and have your friends pool your iTunes purchases is a nice way to stay within the bounds of iTunes DRM.