"Titular" is an English adjective meaning "in title only, as opposed to reality." E.g.: "Following the Glorious Revolution, the descendants of James II were the titular monarchs of England."
It has a rarely used (in formal written American English) secondary meaning, "of or pertaining to the title of something." E.g.: "Binx Bolling is the titular character of Walker Percy's novel The Moviegoer." The much more common and clear way to write this sentence is: "Binx Bolling is the title character of Walker Percy's novel The Moviegoer."
In quizbowl, the word "titular" used where "title" would have been much more appropriate became a meme around 1998, possibly due to HILARIOUS! evocation of a slang term for the female breasts. The intentional use of the word to provoke giggles (or, perhaps, tittering) subsided by 2003. Unfortunately, ever since 2010, a non-ironic use of "titular" has once again exploded as part of the quizbowlese phenomenon. In literally every case, it is better to use "title" as an adjective or consider whether multiple references to "the titular/title character" in your question are helpful in the first place.
Neither word is appropriate to use when referring to "the titular event" or "the title phenomenon" in history or science questions that are not on formal and unambiguous published titles of creative works; the proper remedy when tempted to do this is to jump off a bridge.