Money, or more specifically, currency has value only because others will accept it in exchange for goods or services. The reason why these pieces of paper, plastic, and base metal the governments of the world call dollars, euros, yuan, yen, francs, etc., etc. have value is not because those governments say they do but rather because those governments will accept them in payment of taxes, fees, and other amounts of money owed to them. From that one fact all else follows.
So, let's follow the logic, Bitcoins are not issued by any governments. Furthermore, as far as I know, no government will accept them as payment for taxes or fees. However, because there exists an exchange for the buying and selling of Bitcoins using government-issued currencies, they have value but only relative to the values of the other currencies. You can think of it in another way, Bitcoin is almost exactly the same as buying gold and silver bullion coins. Because no government uses the gold standard anymore or issues gold or silver coins for general circulation, the value of gold and silver in relation to the dollar or the euro, for example, also varies.
But the value of Bitcoins also is dependent upon the security of the place they are stored. If your Bitcoin wallet can be easily picked, you are going to value them less. You will view dollars deposited in a bank whose deposits are not backed by the government in a similar light. This happened during the Great Depression when people kept their money in their mattresses and other places. While a mattress may not be a secure place to store money, people viewed their mattresses as more secure than the banks that were going bust left and right at that time. The same can be said about gold. You can buy gold and pay someone else to store it securely, someone with insurance. But I can keep it myself under my proverbial mattress if I choose. And the same can be said about my 401K retirement account. It's with a reputable brokerage (well, if you can use that word to describe Wall Street shysters) and my account is backed by insurance. I expect it to be there when I need it. But I can if I choose get everything on paper and put it with the gold to keep it company. But Bitcoins do not exist physically. There is nothing I can stuff under the mattress. And there lies the ultimate problem I think.
Well, the largest Bitcoin exchange is dead, 3/4 million Bitcoins have gone missing, and those who owned them are now out of luck. Do I trust them? What do you think?