I noticed that this word get used often in the speedrunning community, but I never understood what it meant.

For example: "I been trying to grind out the game." "I've been grinding to beat my personal best." "I've been interested in the GTA grind."

Can anyone tell me what does it mean?

Grinding means trying to shave off any time of the PB/WR by playing the game as much as possible. Can be very frustrating, so many speedrunners don't do it.

Also can be about "grinding out a tough trick" which would be about continually doing a section to get better at executing a certain technique. But in general it's just about doing something for a long time to try and do it consistently or to get a faster time.

SRL also has some other speedrunning terms defined here if you need a place to check for other stuff: http://www.speedrunslive.com/faq/glossary/