Waves are worthfull, they have value because they are useful and because they are scarce. When we say that a currency is backed up by gold, we mean that there’s a promise in place that you can exchange the currency for gold. Waves, like bitcoins, dollars and euros, are not backed up by anything except the variety of merchants that accept them.
The price of Waves is determined by supply and demand. When demand for Waves increases, the price increases, and when demand falls, the price falls. There is only a limited number of Waves in circulation and new Waves are not created, which means that higher demand will make the price go up. Because Waves is still a relatively small market compared to what it could be, it doesn’t take significant amounts of money to move the market price up or down, and thus the price of a Waves is still very volatile.
Alternatively it needs to be added that while the law of supply and demand applies it does not guarantee value of Waves in the future. If confidence in Waves is lost then it will not matter that the supply can no longer be increased, the demand will fall off with all holders trying to get rid of their coins. An example of this can be seen in cases of state currencies, in cases when the state in question dissolves and so no new supply of the currency is available (the central authority managing the supply is gone), however the demand for the currency falls sharply because confidence in its purchasing power disappears. Of-course Waves do not have such central authority managing the supply of the coins, but it does not prevent confidence from eroding due to other situations that are not necessarily predictable.