To put it semi-mathematically: A Goal is a mathematical function that a system seeks to maximize.
Or, just about equivalently: A Goal is a state of affairs that a system seeks to cause to occur.
Trickiness of Defining "Goal"
This is actually a fairly difficult concept to fully mathematize, because it is difficult to define "seek" if one has not first defined "goal".
One can fairly easily define the goals a system has achieved in hindsight -- what functions the system has maximized over its past history. However, it is harder to say what functions the system is seeking to maximize. For example, a 15 year old may have a goal of becoming immortal, and then get hit by a car and die -- but that doesn't mean he didn't have the goal, even though he came nowhere near to maximizing the function defining the goal (lifespan).
Explicit and Implicit Goals
One way to define the concept of Goal more precisely is to introduce explicit versus implicit goals.
One may define an Explicit Goal as a goal that is explicitly represented inside a mind, as a function that the mind knows it is trying to maximize.
One may also define an Implicit Goal of a system as something that the system looks, to a very smart observer, like it is working toward.
In the case of the 15 year old immortalist, immortality may be both an explicit and implicit goal.
In the case of a confused person, implicit and explicit goals may be out of synch. The explicit goal -- what the person thinks they are seeking -- may be different than what an intelligent observer would see they are actually seeking. This is rather common in human affairs.
In general, alignment of explicit and implicit goals is one aspect of Self-Actualization; and also a characteristic one would like to see any mind capable of Strong Self-Modification possessing, as a prerequisite to Friendly AI.
Mind Ontology Links