Pulleys can do a magnificent thing. They change the direction of gravity.
Gravity is a force that naturally always pulls down. It is a force that exists only on the Y axis when it comes to two dimensional kinematics.
Lets say spider man is hanging from a pulley. If you were to draw a free body diagram of the pulley on the roof top it would include: the force of gravity going down, Normal force (equivalent to the force of gravity) pushing up, and tension pulling to the left. Spider man's free body diagram would have the force of gravity down, and tension to the left. Now I know I said gravity will be altered and here it is: we must combine these two diagrams to find the net force, or the total force applied in the scenario. The tension from the pulley lies on the X axis, but the tension from spider man is on the Y axis. We cannot compare apples to oranges, so we have to make these two tensions some how equivalent. Imagine taking the free body diagram for spider man and rotating it clockwise. Now the tension is running along the Y axis where we want it to be so we can calculate the net force of the two objects combined. However, in turning the entire free body diagram the force of gravity that was vertical is now running horizontally. In essence, the gravity on spider man has a side ways pulls.
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