1. In videogames, collecting a certain item (usually a currency) in order to power one's character up.
2. In Maple Story, killing monsters for mesos and items to sell.
3. (Although it is quite obscure) In Call Of Duty, when one lures other players to oneself and camps in order to take in a massive amount of kills. Usually some type of SMG or MG is required for this farming.
1a. I powered my Soma up in Dawn of Sorrow by farming a bunch of bat and golem souls.
1b. My Dante is teh shit after I farmed a couple dozen hundred red orbs.
2. D00d! You're a total farmer with those Stiff Feathers and Horny Blue Mushroom Caps.
3. Bwahaha! All n00bs will feel my wrath in COD. I are the best farmer evah!