What are the duties and responsibilities of the Quartermaster?

Answer 1

In the the army the Quartermaster is the one individual or combined unit that supplies and provisions troops. The Quartermaster Corps is responsible, for example, for supplying all the petrol for the army's cars.

At sea (i.e. naval usage), a Quartermaster just refers to the navigator of the ship. S/he is in charge of driving the boat

Answer 2

A quartermaster in the army is in charge of distributing supplies, such as ammunition and uniforms, to the troops. This person needs to keep track of what is in storage and what needs to be ordered. A quartermaster in the navy is in charge of navigation of ships. This person will need special training and the ability to use all sorts of navigation devices.