I would guess, although I don't know, that the post you have seen would be the person responsible for the budget of the parish council. They have a very small (if any) staffing establishment but do have some functions. I live in an area with county, district and parish councils and the responsibilities are listed on the county council website.
Another guess is that the clerk would arrange meetings of the council, publish the agenda, minutes and ensure that decisions made by the council are carried out.