Although Bitcoin is not backed by a physical asset like gold, it is worth noting that the United States dollar and virtually all contemporary fiat currencies are not either, or rather, they are backed by political honesty. Bitcoin was designed to be scarce, which helps it resist inflation. Inflation can occur in fiat currencies when they are printed in large quantities, diluting the existing supply.
Reality
There will only ever be 21 million bitcoins. Scarcity is the main cause of its value. Not only is the supply controlled, but the amount of new bitcoins mined has been decreasing over time in a predictable way. Every four years, an event called halving occurs, in which the rewards paid to network miners are cut in half. This ensures that the supply is always decreasing. By the basic economic principle of scarcity, halving keeps the price of Bitcoin on an upward trend in the long term.
Bitcoin also derives value from the work that the computers on the network do in a process called mining. Powerful computers all over the world perform a huge amount of processing work to validate and secure each transaction (in return, they are rewarded with new bitcoins).