Typically, organizations use their human resources or personnel department to create job description templates. In some cases however, a departmental group, a manager, or another individual (usually the direct supervisor of a position) might be responsible for creating one. In any case, make sure the creator of the template is familiar with the company’s or organization’s needs.
The term ‘job description’ is a flexible one, but here I’ll be using it in a modern context, to describe all of the copy you’d use on an online job board. It usually includes information like job title, duties, salary, etc.