Fiat money is money that has no entity backing it other than the issuer, usually a government. When the United States dollar finally disconnected from the gold standard in 1971 it became a fiat currency. Basically the USA declared, "The dollar has value because we are 'Murica" and the world said, "OK". In actuality, the US dollar has no intrinsic value other than the fact it is issued by the United States. Most modern currencies are fiat money.
Bitcoin follows the same principle, in that its value is determined by perception. Instead of the trust of some government entity being evaluated to determine the value of Bitcoin, other factors (the technology, widespread acceptance, understanding of e-money, etc.) are taken into consideration. When magazines and online entities write intriguing articles about Bitcoin, people take interest in it, the demand goes up and so does its value v. government-back currencies. Likewise when Mt. Gox is DDoSed, a bitcoin service shutters, or $250,000 worth of BTC is stolen, people get nervous, demand drops, and so does BTC's value.