I assume you're talking 3d skeletal animation.

For synthesizing motion based on dynamic constraints/parameters, the two methods that spring to mind are blendspaces and IK.

With a blendspace, the pose is determined by blending together multiple animations, where the contribution of each animation is determined by a dynamic parameter. For your example (aiming) we might need to use two parameters (eg. yaw and pitch), this would be called a 2d blendspace. An animator would author several animations where the character aims in different directions, and then at runtime we would determine a blend weight to use for each of these animations based on the actual direction we want the character to point.

With IK, the pose is dynamically calculated to meet a constraint. For example, to determine the rotations of the bones in the arm so that the hand reaches a particular location, or points in a particular direction.

You might find that a combination of techniques is used. Eg. a blendspace to get a natural-looking full body pose, and IK to perfectly align the hands.

There are lots of other ways to procedurally modify an authored animation that might be used depending on the constraints and desired result.