The answer comes from understanding that every form of money, from dollars to gold to bitcoins, is only valuable if people consider it to be valuable. A money’s worth is completely based on our own individual perceptions. If we trust and value a form of money, we’ll accept it in return for our own goods and labor. But our trust in particular forms of money is not arbitrary or without reason. Nearly every form of popular money in history has possessed particular traits that have caused people to want to use it.
Bitcoin has nearly all of the properties of secure, sound, and useful money. And if a new form of money possesses enough of these qualities, especially to the point where it’s advantageous to use over other existing forms of money, people will voluntarily choose to accept it as payment and hold it as store of value. As demand increases, value increases, and the exchange rate goes up.