I would think tension is like a normal reaction force. For example, if a rope is held vertically with a weight on the end. There is a force acting on the rope opposite in direction to the force that gravity exerts on the weight. That force is tension.
Well I do not know where I can get visual representation. But think of it like this;If you have a weight suspended from a rope, and the rope-weight system is in equilibrium. Do you agree that the weight acts vertically downwards?If so, for the system to be in equilibrium should there not be a force equal and opposite in direction to the weight?