Rush: Trying to decide the game early by attacking quickly.
Harass: Attack quickly with a small amount of units, but not with the aim to decide the game, but to disturb the development of the enemy. Harassing often involves trying to disturb the economy or trying to steal xp or items when the enemy is creeping.
Micro: Controlling your units in a battle. For example using spells, retreating hurt units or focusing fire on a weakened unit to prevent the enemy from retreating it.
Macro: The development of your economy. For example: gaining wood and gold at a high rate, upgrading your units.
Focus Fire: Focusing all ranged units attacks on a single unit to kill that unit as fast as possible.
Nuking: Using focus fire and all spells on a single hero to kill that hero as fast as possible.
Creeping: Fighting the various creeps around the map to gain experience points and items.