The Focus Puller, also known as the First Assistant Camera, or 1AC, is responsible for achieving the correct focus for every camera set up. 1AC's have a lot of responsibility on the set, and for the production.
The 1AC is part of a larger camera department. The 1AC typically will calculate the correct focus for a particular shot by measuring the distance from subject to the lens sensor or film. You'll often see them with a range meter or laser or a good old fashioned metal tape measure.
You'll also see the 1AC with some colored gaffer's tape to help them with spots on the set to corresponding notes on their physical ring.
With really large budget shows, you may even see a focus puller using a remote device, rather than hanging off the side of a camera. See https://shop.redrockmicro.com/microremote/ for examples.
Focus pullers get a real workout when they're required to 'pull focus' or 'rack focus' during a particular scene.
At the end of the shot, or when the director yells, "cut", the Focus pullers are also responsible for 'Checking the gate' - which is to look for hairs or broken film which would ruin the shot. In the modern era, this is usually accomplished by checking the sensor. If there's anything wrong, they'll have to shoot the scene or shot again.