Bitcoin is the solution to the double-spend problem.

This means that when you send bitcoin, the receiver can be sure that you actually owned the bitcoin you sent, and, that once you sent it to them you cannot spend those coins again by sending them to someone else (double-spending).

Just like me giving you an orange. Once it leaves my hands and is in your hands, I no longer have the orange to give to someone else.

..double-spends are never accepted into the transaction pool, so every node bears witness to which transaction it saw first by working to put it into a block.

~ Satoshi Nakamoto 2010-12-09