A frequent theme on the show was his discovering an entangled deception of his wife's, whereupon he'd intone sternly to her: "Lucy, I think you've got some 'splainin' to do."
Today people use the phrase both as a fond allusion to a cherished TV show, but as a way to imply that another person is at fault with something and needs to come clean.
Example 2. My Rolex, my computer and my car are all gone... and you've got a bad heroin problem? I'd say you have some 'splainin' to do!