Headphones are really useful for lots of applications, but as a musician they are great for recording, tracking, practising and low volume rehearsals. With a decent set of headphones, you can practice the guitar at any time without disturbing anyone.
Monitors aren't like the pc screens, in an audio application. Monitors are usually speakers 8” or smaller that are designed to show what a recorded piece of audio sounds like, in its truest form. These speakers are not to make something sound nice, like most HI-FI speakers but are actually designed to show issues with the audio you're recording.