Look at the diagram above, there are 2 pulleys, 1 of which is fixed the other which is free to move. There is a wire running from a mass all the way over the 2 pulleys back to an anchor in the ceiling.

These pulleys are the ideal frictionless versions. The free pulley acts like a mass, the anchored pulleys' mass does not concern us.

A question, if the red mass falls by 1 meter what else changes in the system?

The free pulley rises !! Ah ha!

How much does it rise? Well the wire is inextensible and so 1m of wire will come over the anchored pulley, hence there will be 1m less wire on the Left. As the mass drops the free pulley is forced up! The distance it is forced up is half of that of the drop of the mass, because the distance of the drop in the mass = less distance of wire to the left. The pulley is however forced up but using 2 parts of the same wire so although a 1m has gone over the anchored pulley, this 1m is divided into 2 parts by the pulley leaving the increase in height of the pulley at 0.5m.

Does this make sense to you ?