The community.livejournal says this idiomatic expression is used to describe something that pleases you or strongly engages your interest. As I expected, it is also a euphemism for sexual interest. “Tickle” means a spontaneous excitement such as when someone is physically tickled. “Fancy” can be a notion or whim. The expression was used in Abraham Tucker’s 1774 In the Light of Nature Pursued, with a passage about animals “…whose play had a quality of striking the joyous perception, or, as we vulgarly say, tickling the fancy.” The expression went even further to the vulgar side after World War II, when the slang for a male homosexual “Nancy” was noted to rhyme with “Fancy.” An alternate is “strike your fancy.”