This cover is like a multi-layered puzzle you eventually figure out by listening to the album. Even then, questions remain:
1) Is that a light bulb or something sticking out of the top of his hat?
2) Is that actually Captain Beefheart on the cover?
3) Is that a real trout's head or a really good simulacrum?
4) Why is he cradling it in his hand as if to give it a jaunty "hello" mime?
5) OK, I get that it's a replica of a trout mask. But why would someone need a trout mask to begin with? Furthermore, does this imply that a trout mask uses a real trout, while a replica uses an aforementioned simulacrum?
Yeah, I know it's an absurdist, surreal picture that isn't trying to make sense. One of the things I love about album covers is that they can be vague or abstract and leave a lot up to the viewer. Trout Mask Replica is definitely this way, and I enjoy puzzling over it even though there are no answers to be found.