Giddy and dizzy due to falling in love.
As far as I can find, this word was coined in the Disney movie Bambi. The owl used it to refer to those just falling in love.
A combination of the words twitter (to confuzzle) & pate (referring to the head). It means one is smitten, love-struck, and is a bit doolally because of this. It is closely related to addle-pated, but much nicer.
These days the words twitterpated, twitterpate, and twitterpating are used in a number of contexts, including getting high, getting horny, and getting flustered. This is to be expected with any funny-sounding word that has not yet entered the dictionaries and school-houses, but I am happy to report that for the most part, twitterpated and its conjugations are still mostly used to refer to giddy love.
Thanks to Sammy.
An update: as of January 2007, http://onelook.com/, a search engine of on-line dictionaries, finds three dictionaries that include twitterpated.