Yes, ‘fuller’ is indeed a word. It is the comparative form of the adjective ‘full,’ which means containing or holding as much or as many as possible. For example, ‘This glass is fuller than that one.’
Additionally, ‘fuller’ can also refer to a person whose occupation is to full cloth. Fulling is a step in woolen clothmaking that involves cleaning and thickening the cloth. For example, ‘The fuller worked diligently to prepare the fabric.’