Attacking is the act of declaring one or more of your untapped creatures as attackers during your combat phase, sending them to deal damage to an opponent, a planeswalker, or a battle. Creatures usually tap to attack (unless they have vigilance), and they generally can't attack the turn they enter unless they have haste or have been under your control since your last turn.
The most common misunderstanding: declaring an attacker is a special action, not a triggered ability, and "attacks" triggers fire after attackers are declared—you don't choose targets for those triggers until that point. Also, a creature is "attacking" the whole combat, even if the defender it attacked leaves; and being blocked doesn't stop it from being an attacking creature.
In Commander, you choose which opponent (or their planeswalkers) each attacker targets individually, so you can split your forces across multiple players in the same combat—key for politics and racing.