These are omse general game mechanics which you should familiarize yourself with to better understand the different champion skills, stages of the games, and to get better map awareness.
Ace - Signifies that the entire enemy team has been wiped out. Also known as Genocide in Heroes of Newerth, this is an excellent time for your team to assault the enemy towers or base. To score an "ace" is to kill the last remaining enemy champion when all others are dead.
AD - Attack Damage. This boosts physical-based abilities by a certain multiplier and also determines the damage you will do with one auto attack.
AOE - Frequently seen in more traditional MMORPG's, it means the same here. Area of Effect, an ability that covers an area rather than a specific target.
AP - Ability Power. This is only seen in League of Legends, and it directly boosts many of the magi-based abilities in the game by a certain multiplier that varies by champion, skill, and level.

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Aura - An ability which is usually passive and buffs allied heroes or debuffs enemy heroes in close proximity. Sometimes auras may have costs associated with activation or upkeep.
Backdoor - To attack an enemy tower or base location while the rest of your team is engaged in a fight, usually 4 versus 5. The risk to doing so is great, but the reward of pushing another lane or tower/inhibitor can be great if done correctly and your team can hold its own without you.
Barracks/Racks - The spawning location of the creeps inside a base. When these are taken out, the creeps of the destroying team will get much stronger, allowing them to push deep inside opposing territory and possibly kill characters by themselves. In LoL, this is the inhibitor which spawns Super Minions.
Bottle - An object found in Heroes of Newerth and DOTA, it can be used to "bottle" runes, allowing them to be used when they will confer the most benefit.
Brush/Bushes - Foliage which provides the ability to hide. Only found in League of Legends. Some champions gain a passive ability when running or being in a the brush such as Cait's headshot attack or Nidalee's speed boost.
Buff - Something that boosts stats or abilities, generally for a set duration of time, although some are permanent. This could also refer to the improvement of a champion following a patch.
Carry - A character that can eventually "carry" the team to victory. Typically has scaling abilities which allow him to take on multiple heroes at the same time, sometimes entire teams. They are usually more squishy (eaiser to kill), but are capable of putting out a lot of damage.
CC - "Crowd Control". Includes moves that stun, slow, fear, blind, and anything else that may impair movement or disable enemy opponents.
Champion/Hero -The character you play for the duration of a game.
Channel - The act of temporarily losing the ability to move or attack in order to activate a skill. Most channeled abilities are very powerful and can be broken with a stun or disable. The progress of a channel is displayed in a bar on the bottom of your screen.
Creeps - Traditionally refers to the game-spawned armies from each team that flow mindlessly toward the opponents base within a lane. See also Neutrals.
Cooldown (CD) - The duration between when you can cast the same spell again. Spells that do more damage (such as ultimates) usually have longer cooldowns.
DD - Direct Damage. An ability that is basically "point and click" to result in X amount of damage to an opponent as long as they are in range. In LoL, this is referred to as True Damage (damage not mitigated by armor or magic resistance).
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