A hackbike comes from the term 'hack', short for hackney, used for a horse that was used for everyday use - most specifically for a gentleman to ride to to a hunt while his groom left earlier and rode his good quality hunting horse there at a gentle pace. The hack was a sort of second best horse, to be used a little more roughly, often hired (hence Hackney carriage, a carriage pulled by a working horse as opposed to a smart carriage horse, and in today's terms, a hired vehicle). Today, hack also means to go for a ride in the country with no particular purpose other than the ride...
I believe it comes from a French term originally.
So a hack bike is your everyday bike, the one you don't mind getting a bit wet and dirty, as opposed to your fancy best bike.