Action is what any agent can do.
For example, throwing a ball is an instance of action; it involves an intention, a goal, and a bodily movement guided by the agent. On the other hand, catching a cold is not considered an action because it is something which happens to a person, not something done by one. Generally an agent doesn't intend to catch a cold or engage in bodily movement to do so (though we might be able to conceive of such a case). Other events are less clearly defined as actions or not. For instance, distractedly drumming ones fingers on the table seems to fall somewhere in the middle. Deciding to do something might be considered a mental action by some. However, some think it is not an action unless the decision is carried out. Unsuccessfully trying to do something might also not be considered an action for similar reasons (for e.g. lack of bodily movement).
It is contentious whether believing, intending, and thinking are actions since they are mental events. Some would prefer to define actions as requiring bodily movement (see behaviorism). The side-effects of actions are considered by some to be part of the action; in an example from Anscombe's manuscript Intention, pumping water can also be an instance of poisoning the inhabitants. This introduces a moral dimension to the discussion (see also Moral agency). If the poisoned water resulted in a death, that death might be considered part of the action of the agent that pumped the water. Whether a side-effect is considered part of an action is especially unclear in cases in which the agent isn't aware of the possible side effects. For example, an agent that accidentally cures a person by administering a poison he was intending to kill him with.
A primary concern of philosophy of action is to analyze the nature of actions and distinguish them from similar phenomena. Other concerns include individuating actions, explaining the relationship between actions and their effects, explaining how an action is related to the beliefs and desires which cause and/or justify it (see practical reason), as well as examining the nature of agency. A primary concern is the nature of free will and whether actions are determined by the mental states that precede them (see determinism). Some philosophers (e.g. Donald Davidson) have argued that the mental states the agent invokes as justifying his action are physical states that cause the action. Problems have been raised for this view because the mental states seem to be reduce to mere physical causes. Their mental properties don't seem to be doing any work. If the reasons an agent cites as justifying his action, however, are not the cause of the action, they must explain the action in some other way or be causally impotent.