A sea spider is a spider that dwells underwater. The only physical appearance of a sea spider is in "Patrick's Coupon" where Patrick encounters one.
The sea spider looks similar to a sea urchin. In "Patrick's Coupon," they look very similar to real spiders with a grayish body and red eyes. The spider's legs are hairy and are extended to suit the body. They also have a gland on their abdomen to spin out webs. Sea spiders have monstrous teeth, most likely meant for their prey and predators. They have eight compound eyes.
The sea spider is mentioned several times. SpongeBob and Patrick think that Squidward's wig is a sea spider, and smash it with something whenever they see it.
In its only physical appearance, the sea spider fights with Patrick at the beginning of the episode. After making peace with the sea spider, Patrick finds the ice cream coupon that starts the episode's plot.