Imagine an object that's fixed at one point but free to rotate. Give it a push. It can't move laterally, since it's fixed at the pivot, but it can begin to spin round and round. Analogous to Newton's laws of linear motion, there's a set of equations governing how fast the spin rate of the object increases. Check out Tipler (p. 227) if this is new to you.
In rotational motion, Torque plays the same role as force in linear motion. The torque () is defined as the force multiplied by the perpendicular distance between the force and the pivot.