Economic equilibrium, where supply and demand are balanced.

Currently crypto-currency markets are quite illiquid. This makes the price of bitcoin and other cryptos fluctuate a lot. The uncertainty around them does not help either. Regulation, technical challenges, reputational issues and other factors make the supply and demand unpredictable.

Based on what does the price go up or down? I would say it is based on people's expectations. If they expect the price of bitcoin to increase due to a utility increase over time (more merchants accept it, transaction volume grows, there is a larger ecosystem of developers building on top of it...) there will be a rise on demand, and assuming that the supply does not increase in the same proportion, the price will go up. On the contrary, if the utility decreases (mobile platforms block crypto apps, technical issues arise, governments ban them, exchange markets get shut down...) the demand will decrease, the supply will increase (more people willing to sell) and the price will go down.

In the long term their value will be determined by their utility (adoption by merchants and other users, significant advantages with respect to other forms of payment...), liquidity (exchange markets, interchangeability with other forms of value...) and trust (reputation, regulation, adoption by trusted institutions...).