Bitcoin is really two ideas: an unforgeable digital datum based on "proof of work" or "hash collision" ideas; and a global, decentralized, distributed database to keep track of which data tokens have been "spent". The tokens don't yet have any true monetary value, but due to the design of the system, only a finite number of tokens will ever exist, so they would be candidates for being the basis of a monetary system. IOW they might be worth something someday.
The interesting part is making the global DB immune to attack or takeover. Bitcoin relies on the long tail effect. The total compute power of the great number of honest users must outweigh that of a well-funded attacker. So long as this is true, token forgery is impossible.