The bitcoin's value is the computing power that was used to create/solve it, and the cost of that computing power.   This creates a competition of who's computer or cluster of computers can solve the problem the fastest and least costly, which generally excludes all consumer CPUs and GPUs and requires specialized computing units created specifically for solving bitcoins.  

 

But the most celebrated property of the bitcoin seems to be the blockchain.  Every transaction ever made on bitcoin (whether purchaces or anything else) is stored on the blockchain which is readily available to anyone.  Because of the perceived impossibility to forge the blockchain, it is seen as a breakthough technology that didn't exist before bitcoin existed.

 

(not a bitcoin expert, or even a user, but that is my best explanation)

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