If Bitcoins aren't tied to a conventional currency, how did they get so valuable?
I think initially there was utility for crypto currencies in 3 major areas which fueled its rapid rise
The first area is the unbanked demographic. There are many around the world who cannot meet the minimum balance to have a bank account. Crypto currencies give this demographic a way to execute electronic transactions without having to jump through hoops to meet the demands of banks.
The second area are crypto funded darkweb markets like silk road, alpha bay and hansa. While many of these were shut down in 2017 and no longer have much impact on the value of btc as they once did. They are a big part of crypto currencies history and in previous years represented a significant portion of bitcoin value.
The third area is bitcoin's relatively low transaction fees in comparison to many services offered by banks. Some countries like cuba are known to charge ridiculous fees and taxes on wire transfers going into the country. American immigrants from cuba would need a method to send money back to their cuban families. Bitcoin gave them a way to achieve this without having to pay 40% taxes/fees or whatever the going rate was.
In countries like africa we often see bitcoin trading substantially higher than other countries. The reason for this is due to bitcoin offering substantially lowering taxes and fees on things like wire transfers and electronic banking services. Bitcoin is much cheaper than its alternatives which is why africans are willing to pay more for bitcoins.
Keep in mind, this is a general overview off the top of my head. I might have missed a few things. The historical price of bitcoin and its design revolving around algorithmically limited supply which makes it virtually impossible for it to be hyperinflated like fiat money along with btc being deflationary are all contributing factors as well. As is the revolutionary design of bitcoin utilizing blockchain which has many real world applications. Bitcoin's ease of use, convenience and security measures also play a large role. As does the way transaction costs compare to traditional banking services.