The textbook example of fractional reserves:
You are a bank. Sally gives you $100, so now you have $100 in cash as assets. Bob comes up to and asks for $80. You agree to give him $80, on the condition that he gives you $90 next week. Now you have $20 in cash and a $90 loan backing your $100 liability to Sally. Because that $20 in cash is less than $100, you have fractional reserves.
Now, the real world is more complicated, because there's different definitions of cash and of liabilities, and even questions like "how much is this thing worth" can be very hard to pin down. But the basic idea of fractional reserves is that banks do not hold all of their reserves in cash.
And yes, the cryptocurrency industry does cater heavily to people who find the existing banking system abhorrent because it practices fractional reserve banking while practicing fractional reserve banking themselves, just far more quietly. (Indeed, a lot of the cryptocurrency industry is basically preying on people who are financially illiterate.)