ABM:
ACS: Alliance combat system allows for friends and alliance members to temporarily combine their fleets to  defend a target that either might not have been able to defend alone.
Bashing: When attack any given planet or moon owned by a player for 5 times in a single 24 hours period.(Check rules at Zorg site for a detailed explanation.)
Fleet save: When you send your ship on a mission when you are offline so nobody can destroy it.
IPM: Interplanetary Missle.
MILK: Sending resources to a higher ranking player.(Not permitted in Zorg unless you do it in the trade parameters)
Pull: Once within a 24 hour period a higher ranking player may send the equivalent of 1 hour of production to a lower ranking play.
APP: Application, this is the process of applying for an alliance and can be carried out through the alliances page. *Thank you Istalris for this one*
CIRC: Circular Message, the message system used to send a message out to everyone in your alliance at once.
NAP: NonAggression Pact or NonAttacking Pact - People or Alliances who have a NAP don´t attack each others.
PPM: Points Per Member -Average points per member in the alliance statistic view.
TAG: The alliances shortened name, symbols, or abbreviation thereof. (ie: the tag DR = Death Riders) *Note in the Galaxy view you will see a column that says alliance. There you will see the TAG of the alliance. To view the alliance name you can put cursor on the tag and it will pop up another window.