At the end of the story, after Henry has tried to persuade his brother Lyman, the narrator, to take and keep the red convertible they have shared for many years, Henry jumps into the river, he says, to cool himself off. Henry's behavior has been the most typical of his old self since he returned from fighting in the Vietnam War. He has spent the last several months working on the car and trying to get it back into tip-top shape after Lyman wrecked it on purpose, trying to give his brother a reason to want to live.
After Henry jumps into the river, Lyman can see that the current catches him and pulls him farther out. Henry shouts back to his brother, "My boots are filling." Literally, he is referring to the water filling up his boots, how it is weighing him down and making him sink into the depths of the water. Figuratively, he probably means that the pain that he feels, the way the war changed him, and the things it showed him, are weighing him down emotionally and mentally (rather than physically).
Those feelings pull him down, metaphorically, into depths that he cannot resist, just as he cannot resist the literal weight of the water in his boots. The water in his boots, then, is symbolic: it has both literal and figurative meaning. It is literally present, as his lower half is submerged in the river, but it also figuratively represents the weight of his depression.