The difference is in the way the ear cups are designed. On open-back headphones air is allowed to pass from the rear of the speaker driver, preventing the build-up of any resonances and low frequencies. This is why you’ll find many studio and high-end headphones with an open-back design as it allows for a more natural sound.
The downside of this is that they also allow any external noise in, and if you’re playing at a reasonable volume, your playing will bleed out so anyone nearby will definitely be able to hear those bum notes and out-of-tune bends!
Closed-back headphones don’t allow any air to escape, which means a less natural sound, but much better isolation from the world around you. Closed-back headphones tend to hype the low end of the frequency spectrum but you get to be safe in the knowledge no one can hear you messing up that legato lick for the eighth time.
You’ll find headphones geared more towards regular consumer listening with the closed-back design, as there’s little to no bleed from them. This makes them perfect for silent practice late at night.