Represents wealth yes, but more correctly, it is an agreement. We all agree that this piece of piece of paper with that number on it represents a certain amount of wealth. Which is also exactly what we do with bitcoin.

And most of my friends still ask me - yea but what gives bitcoin it's value. My answer is always, what gives the money in your pocket value. You'd be amazed at home many people still say "it's backed by gold"...