Why would anybody buy bitcoins? They are not considered legal tender in any country, they are not widely accepted as a form of payment, and their value can fluctuate as much as thirty percent in a single day.
The answers are really fairly simple... you even answered one yourself. People speculate in them (your fluctuations), people see the potential of a decentralized uncounterfeitable currency. Some see bitcoins comparing to FIAT as email comparing to the postal service. Some believe in the political philosophy behind a decentralized currency. Others like a currency base that is only BARELY inflationary at first, then eventually stable to deflationary as opposed to the massively inflationary nation backed paper currencies.
They are instantly spendable.
I can send them to an address in ANY country in 10 minutes or so.
They can be relatively anonymous.
Conversely the blockcain (ledger) is entirely public.
Really the advantages the technology behind bitcoin gives us is an idea that will never go away.
This IS the money of the future. Even if "Bitcoin" fails some cryptocurrency will rise to take it's place.