Tension

Whenever a rope exerts a force on an object, a tension T is created in the rope that transmits the force through the rope.

Usually we assume massless, non-stretchy ropes. When we exert a force on such a rope, the rope exerts that same force on the object. Tension makes the rope feel like it's being pulled apart.

Final note: you can pull with a rope, but you can't push with a rope!