They are your toilet's intake and discharge hoses
The valves where both hoses connect to the hull are called seacocks, and they open and close thru-hulls (holes in the hole) that are underwater. If you leave the valves open when you're away from your boat. The small hose is your toilet's flush water intake hose...the larger hose is the toilet's discharge hose. If you leave the valves open when you're away from the boat, water can overflow the toilet and and sink your boat.The small hose is the toilet's flush water intake hose. The larger hose is the toilet's discharge hose. If it goes straight from the toilet to the thru-hull, the toilet is flushing directly overboard, and yes--that's illegal. It must either go into a holding tank or go through a separate treatment device. I've attached a link that I think you'll find useful--"Marine Sanitation: Fact vs. Folklore" explains the laws, the equipment that's need to meet the legal requirements--and how it works--and answers more questions about marine sanitation systems that it ever occurs to most boat owners to ask. In addition to it, I suggest you read the articles in the Head Mistress forum Reference Library (on the forum homepage). There's a little duplication of the material in "...Fact vs. Folklore," but even that has been updated.