I have a woman's cruiser bike with pedal brakes only. Everything has been working great but when I took a bike ride the other day I was on a flat street and it was extremely difficult to pedal...why and what can I do to fix it?
Start with the easier things before busting out the spanners!
Check the bike over. Low pressure tyres are very hard to ride, so add air with a pump.
Look for anything wrong, that's anything rubbing or otherwise out of line.
Walk the bike around and make sure it coasts okay.
Rotate the pedal crank while lifting the rear wheel off the ground and make sure it looks right with no bad noises/feelings.
If it is the back wheel not spinning freely even when off the ground, sounds like your brake may be the cause. A teardown can be a complex and messy thing, how's your mechanical skills?
Final point - if there is only one brake and its not working right, don't ride the bike till its fixed. Many locations require two separate braking subsystems. Where's your front brake gone ? Also, riding it in the current state may worsen a repair into a replacement.
Edit: I agree with Criggie about the check list first, I just assume people check for the obvious, I probably shouldn't assume that though.
What can you do to fix it:
Unless you are happy getting your hands dirty and doing something like in the youtube link below then taking your bike to a bike shop would be the best option.
If you are happy getting your hands dirty then the model of your rear hub/brake is needed to provide accurate information. Until you open it up you won't know for sure if part of the brake is actually broken and replacement parts are needed or if just a service will suffice. However I would guess just a service is needed since you merely found it hard to pedal on a flat and did not mention variations in difficulty or other strangeness.
Why it happened:
You only really find this out while fixing it. It is impossible to accurately answer this with the information provided in your question, however assuming it is because the brake is no longer functioning correctly, I would guess: insufficient grease and/or rusted bearings and/or too much gunk and dirt in the hub.