His main job would probably have involved recording the numbers of all wagons that arrived, together with such other details as needed (origin, destinée, weight, etc.) and recording similar details when they left. All this would be written down in ledgers (*) and only looked at again if there was a problem. He would probably have other jobs, including advising customers when a wagon arrived (unless the Station Master did this), checking when wagons were ready to go, sweeping them out, closing doors, writing out wagon labels, assisting the guard when shunting, etc. The job description checker was just a broad one: the exact duties would be decided for each location.
There were ticket checkers whose main job was manning the barriers at large station, and travelling checkers who worked (mostly) mainline trains assisting the guard by doing the ticket checks.
* - The pre-computer railway created enormous amounts of paperwork, most of which just ended up being ‘filed’ in cupboards.
Mostly based on one of my early jobs, when the morning was spent doing what was then called Numbertaking.