The song's title and the line is an euphemism for having energetic intercourse.

The previous person who referenced these lyrics on your site was being too literal, mentioning Peeping Toms. Remember, this was the ultraconservative '50s. Their sexual references had to be well-hidden. Think symbolism: The 'one eyed cat' reference is the giveaway. Cats obviously LOVE seafood. But why only one eye? Think 'one-eyed trouser snake.' Now substitute 'seafood store' with a woman's private parts (often crudely equated with 'smelling like fish.') You get the idea. Gives a whole new meaning to Haley saying he wants to 'shake, rattle & roll.' Incidentally, Haley was blind in one eye, which gave him something of a 'cover story' for the dirty line. Furthermore, Haley toned down the naughty lyrics considerably from the original blues version written by Charles Calhoun (and first recorded by Big Joe Turner). Haley also recorded his version as more 'rock and roll' - all in the name of making the song more palatable to white audiences.