What is 'grinding' in MMORPG games?

It is where you don't progress anywhere along the main storyline of the game intentionally, you just stay in the same area, etc and battle to gain experience points. When the player decides he/she wants to progress further, he/she will go back to playing along the storyline with the new experience.

Grinding would be doing something repeatedly for a benefit, ie killing monsters for experience, could be roaming around an area killing specific monsters for their loot so something special can be crafted.

The meaning is variable depending on what the grinding is done for.

Doing a repetitive task in order to reach a goal. Such as: I need 100 blue gems. Only Snow Trolls drop blue gems. So I'll need to grind out killing snow trolls until I have 100 gems.

Killing lots of stuff to get experience which is mostly boring because it feels like your grinding your way through the enemies to get XP

Repeatedly killing npc's for experience or gold.

E.g. Spend 3 hours killing wolves, gain 4 levels. You just grinded for 3 hours.

when you go and fight enemies for expirience to level up. Usually this term is used when someone is planning on leveling up a lot for a extended period of time

Training on monsters for experience.