MSQ - Refers to the main Story Quest line.
PST - Please send Tell; used to send private messages to an individual. Maybe just the sound of a whisper, I don't know.
Dow/Dom - Disciple of Hand/Disciple of Magic; refers to the battle capable classes/jobs (see right chart)
FC - Free Company; essentially a guild! It is a community of players that can communicate together & benefit from FC buffs such as EXP gain, as well as sharing housing.
LS - Linkshell; private chat channel for a community often used for specific interests; hunts, raid groups, social.
DF - Duty Finder; system used to automatically create parties of players for a selected instance/duty.
PF - Party Finder; sytem used to recruit or join players for a party, where you may list what you are making the paity for!
LB - Limit Break; a powerful party ability that charges up & has effects depending on which class using it. Tank: party-wide damage mitigation. Healer: party-wide heal (revive with 3 bars) Ranged: attack to all targets in a straight line. Casters: AoE damage skill, Melee: strong single target damage skill.
GC - Grand Company; the 3 main military forces of Eorzea! (Immortal Flames of Ul'dah, maelstrom of limsa, & Order of the Twin Adder of Gridania) You may join one of these and climb ranks after beating Ifrit in MSQ 1v1 20.
Bis - Best in Slot; denotes the single best gear piece for a specific job for each slot depending on stats/benefits.
LoS - Line of Sight; used to indicate a broken line of sight, for example a player gets healed by being in a healer's line of sight.
TP/MP - Tactical Points & Mana Points; The resources used by Physical/Magical classes to use skills. May be merged in ShB.
Enmity - The threat held by a player from ab aggressive monster. Otherwise know as aggro/hate/threat.
Gear iLvl - Item Level; a stat on a piece of gear that denotes the approx. effectiveness of the item. It is NOT the required lvl to equip the gear. Noted in Char. menu right above portrait.
GCD/oGCD - Global Cooldown - Multiple abilities that use a shared time of cooldown before reuse. Off Global Cooldown - An ability which has its own cooldown timer & can be used between GCDs.
AoE - Area of Effect; abilities that do damage or inflict debuffs to multiple enemies, or a healing ability that affects multiple targets.