Most commonly eye strain is caused by straining the ciliary body, the eye muscle responsible for accommodation. The ciliary body is the structure in the eye that releases a transparent liquid (called the aqueous humor) within the eye.
The ciliary body also contains the ciliary muscle, which changes the shape of the lens when your eyes focus on something. This process is called accomodation.
Typically the muscle is strained by keeping it in one position for a long time. In other words eye strain is caused by visually concentrating on one thing or one distance for too long. The eyes tend to strain faster from focusing on near distances as opposed to far distances. Switching between distances rapidly can hasten the strain as well.
The ciliary body is a ring of muscles behind the iris that holds the lens of the eye.
Virtually all head, neck, eyes and sinus pains originate from lack of blood circulation caused by constricted muscles.