Hideousness is the quality of being hideous: extremely ugly, or so unpleasant you almost want to look away. It can be about a face, a building, a colour — anything that looks awful. Though actually, people also use it when something is ugly in a moral way, not just to the eyes: the hideousness of a war, of cruelty, of a lie. In everyday talk you will hear the adjective hideous far more than this noun. 'That's hideous!' is common; 'the hideousness of it' sounds a little more written, a little more serious. Older, more literary English likes the noun; younger speakers often just stay with hideous.