Traditionally, when you think of a trawler, you might think of a small working boat used for fishing. In that, you would be correct. They had deep hulls for storing fish and indeed get their name from their primary function: trawling nets for fish. However, over time they have transcended this single use functionality.
The classic trawler design has now been taken and outfitted with pleasure cruising in mind. For the most part they have retained their full displacement hulls that allow the vessel to plough throw the water, rather than on top, but some even sport semi-displacement hulls.