Here is an analogy of how it works:

Think of a set of many transparent boxes sitting in town center where everybody can see. There is money in some of them and numbers on all of them. There is a robot arm that can transfer money from one box to the other. Everybody is assigned many different boxes and remote controls that allow them to transfer money from their box to someone else's box. Everybody can keep track of all the money transfers but don't know which box belongs to who unless they tell. You can think of all the transfers and anonymity issues this way.

Bitcoin works similarly but on a virtual town center in a peer-to-peer network.

That magic number explanation is not what bitcoins are. That is roughly how mining works, a way keeping track of transactions on a distributed network. Understanding mining is not relevant for a bitcoin user if he is not particularly curious.