The easiest way to think about tension is to consider holding a
weight on a string.(like in the diagram) I exert a force to hold the rope and weight in the
air.
Now, I am in contact with only the top of the rope, so that piece (labelled 1
in the figure below) must
exert a force upward on the piece just below it (2) while (2) exerts a
force on (1) (see Newton's Third Law ). Now, for (3), there is force provided by (2) pulling it up, as well as (4) pulling down on it.
(4) has a force because the (3) pulls up on it and (5) pulls down on it ... and so on and so on
until we reach the last piece of the rope (8). It has no rope to pull up on,
but it is in contact with the mass!
Hence, it must be exerting a
force upward on the mass equal to the force I apply to the top of the rope.

