What benefits does Bitcoin (i.e. cryptocurrency) offer?
I'd say that some benefits of Bitcoin and other cryptocurrencies (i.e. "altcoins"), include:


Decentralization -- which is advantageous for those who are skeptical of monetary policy, runs on banks, etc.
Anonymity, or at least the perception thereof -- with increasingly comprehensive monitoring of transactions (particularly non-cash transactions), those seeking relatively anonymous methods of exchange have traditionally been out of luck in the realm of digital transactions. Bitcoin has widely been regarded as a "digital cash", providing some measure of relative anonymity in online transactions, though this is a decreasingly accurate perception as government databases cataloging transactions grow in sophistication (and some of these databases, such as that of the FBI's, have been opened up to public developers via coding marketplaces like Kaggle). Some altcoins, such as Monero (XMR), add measures to enhance the benefit of relative anonymity.
Portability -- they can be easily stored and transported offline (paper-based hashes or QR codes), on portable media, over the Internet, with or without the aid of a "wallet" or bank-like service.
Region Neutrality -- unlike fiat currency or Eastern-only currencies such as Perfect Money, cryptocurrencies seem to have less bias based on location or language.