In the Bitcoin structure, everyone cooperates to keep a check on everyone else’s money, no central authority is involved. Imagine only $21 million exists in the world, and there also exists a detailed list of all the people who own that money. Everyone, including you (even though you have only $5), has a copy of this list.
When you give $2 to your friend, you must subtract $2 from your entry on the list and add $2 to her entry. After notifying her of the transaction, she updates her list as well. In fact, everyone in the world needs to update the list, otherwise, the list would be incorrect. Therefore, not only do you need to update your friend, but you also need to publicly announce that you are updating the list.
If you tried to cheat the system and send your friend $1000, your cheating attempt would be easy to catch because everyone knows you have only $5 to give. Now, that all transactions are carried out on computers that communicate through the Internet, and replace dollars with bitcoins. This is how Bitcoin works. Pretty simple actually.