An attack action (sometimes called a 'standard attack') is an action that can be performed with either a Standard Action, or as any one of your attacks during a Full Attack Action. Where an attack performed with a Standard Action must be performed with the first (and only the first) attack of a full attack action, an attack action can be performed with any one of the attacks in your full attack action. This means, if you have three attacks in your full attack action, you can perform three attack actions.
If you are not performing a full attack action during your turn, you can still perform an attack action, but doing so requires your standard action. As a result, attack actions are much more flexible during a full attack action, but they behave very similarly to standard actions otherwise.
The most common use for an attack action is (obviously) making attacks. However, you can also 'trade away' your worst remaining attack action of a full attack action to perform one of the Combat Maneuvers that require an attack action (this does not apply to Charge, Grapple, Overrun, Tumble, or Withdraw maneuvers, since they require action types other than attack actions) at any point during your full attack action (i.e., you don't need to use up your best attack actions before trading away your worst one to perform the maneuver, you can do the maneuver early, then finish up your remaining attack actions). Bear in mind that only one combat maneuver may ever be performed per turn (unless you spend an action point, or have some ability that allows you to break this rule).
You can also trade away your worst remaining attack action to gain a bonus 5-foot step at any point during your full attack action. This is in addition to the one 5-foot step you can perform as a free action if you don't otherwise move during your turn. Unlike with combat maneuvers, you can trade away more than one attack action to gain an equal number of bonus 5-foot steps, if you wish.
Once an attack action is 'traded away', whether for a combat maneuver or a bonus 5-foot step, it is expended and cannot be used this round for any other purpose.