Bitcoin, like gold has value because people believe it has value. If people value something, it is “valuable” to them. Often we attribute value to things simple because we can do something with it that cannot be done otherwise.

Bitcoin is different than fiat (Government money) in that there is nobody forcing you to use it (to pay your taxes, etc), or preventing you from using it (as in capital controls, etc).
Bitcoin is neutral: it is indifferent to where you were born, where you live, who you are, what you are buying, etc.
Bitcoin has technical properties which make it much more flexible, programmable and reliable in certain situations, so it has properties which might make it more valuable to someone who needs those.
Most of the value today is speculation because people believe it could replace many sections of our economy currently controlled by banks.
For some people, those are very valuable properties (and there are many more reasons not listed here), therefore they are willing to trade fiat money for bitcoin. That is how the price rises.

The more people put their time, energy, money and creativity into something, the more they value it usually. Therefore people like myself assign a lot of value to it as we are helping the network to grow and become more usable.