LFG or lfg is a shorthand for "looking for group". Less common variants are also used, such as LFP ("looking for party") and LFT ("looking for team").
It is a common abbreviation used by players in the in-game chat to look for a party to join. It is usually accompanied by the reason why they are looking for a group and what they have to offer. Examples include "prot monk LFG FoW" or "SS lfg hm"; the former indicating that a Protection Prayers monk is looking to join a party to venture into the Fissure of Woe, while the latter is usually a Spiteful Spirit necromancer looking to do a mission in hard mode.