Originally: a tendency to mention something for the sake of comprehensiveness or exhaustiveness, rather than relevance (now rare). In later use: a tendency towards repeatedly or habitually mentioning something, especially the name of a person one is attracted to or infatuated with, regardless of its relevance to the topic of conversation.
In later use popularized by Helen Fielding in her 1999 book, Bridget Jones: Edge of Reason.
1950s; earliest use found in Journal of Economic History. From mention + -itis, humorously after e.g. tonsillitis.