Can bitcoins be counterfeited? Traditional currencies have anti-counterfeiting features designed to make them hard to copy, but despite this attempt counterfeit money is a real threat.  Since bitcoins are digital, it's trivial to copy them.  Does this mean that bitcoins can be counterfeited?
There is no such thing as a "bitcoin" that can be copied. Rather, there is a list of all the transactions that have taken place on the bitcoin network and the order they have taken place. Every client has a copy of this list. Essentially, the only way to counterfeit bitcoins would be to spend them in more than one place. This is called a double-spend attack. However, because of the design of the bitcoin block chain (the list of all the transactions) and the way that list is secured by mining, this requires a tremendous amount of computer power.

http://en.bitcoin.it/wiki/How_bitcoin_works#Double_spending

See also the question about how mining works

What exactly is Mining?