Who are the Quantity Surveyors?

Quantity Surveyors do exactly what their title suggests.

They work out exactly how many bricks, girders, windows, doors etc., it will take to complete a planned building.
The architect has the idea and produces the plan, the QS takes that plan and works out what quantities of material it will take to build the thing.

A well known American quantity surveyor on the job:

One of his duties: counting apples!