Gold has some utility or purpose (ie jewelry, artwork, etc) but most of its value comes from people agreeing that it has value. They recognize it is fairly limited in quantity (only about 1% inflation annually due to mining) and is physically beautiful. Bitcoin is more rare because we can never have more than 21 million in circulation. After the last coin is mined, no more inflation. Obviously it does not have physical beauty since it's digital, but it has value due to its limited quantity. Just like fiat, it has value because people agree it has value. The difference, and it's a big one, is that fiat is unlimited and bitcoin is not. Banks and the government can make the money supply whatever they wish for any reason or no reason at all. Nobody has that control over bitcoin. Other cryptos have value for their utility as well. Whereas bitcoin was meant to be digital currency (although now it's more a store of value), other cryptos such as Ethereum (smart contracts, decentralized applications), Ripple (cheap payment protocol for banks), Litecoin (digital silver), etc have value for their specific purpose. Hope this answers your question.
RE: Why You Should Be Interested in Cryptocurrencies