Bitcoin’s value is given by the merchant who is willing to exchange it for something of economic value to you (goods, services, etc). These persons who are willing to trade with you for Bitcoin are considered the "economic majority", as they decide which Cryptocurrency definition they are willing to trade value for. The economic majority is the group of persons backing Bitcoin or other accepted Cryptocurrencies.
The US dollar value in contrast is guaranteed by legal-tender laws: Dollars are always accepted for paying taxes, and that reflects a value that will always remain, even if the entire economy decides to stop accepting the US dollar. Dollars are NOT backed by gold.