How does Bitcoin have any value?
That is an excellent question, and one I have been asked in real life by friends, and it's not easy to answer. The short simple answer is that it has value because there are people willing to pay for it. People are willing to pay for it because they think it will have more value in the future.
But what is actually backing Bitcoin up?
I believe it's mostly the technology and the fact that many people are involved in it. With that said, there are other coins which have taken the block chain concept one or more steps further, improved on the technology. Some of those coins will eventually replace Bitcoin in my opinion. But for the time being, and probably the next few years, Bitcoin has the first mover advantage, and it's the only cryptocoin most people know about at this point.
Another thing adding value to Bitcoin is the infrastructure that has developed around it. There are more and more services out there which take Bitcoin in payments or even exist because of Bitcoin, such as
Coinbase, BitTrex, Poloniex and numerous other exchanges.
With all that said, there are still aspects of Bitcoin that are backed up by the current interest of more people and speculators. Right now they want in, so the price goes up. But if their interests go elsewhere, then the price goes down. So for that reason, Bitcoin could also be a bit of a bubble, so you need to invest with caution. I would also recommend getting educated on the other cryptocoins and diversifying into some of them as well.