Turn fanciful around and you get "full of fancy," which gives you the gist of the meaning. The adjective refers to something not quite real, usually something with a whimsical or even dreamlike quality.
The adjective fanciful sprang from the 15th-century noun fancy, which was in turn a short version of the word fantasy. All three words contain the same elemental meaning, that of something unreal. Someone who is fanciful usually allows creative thought rather than the practical to come to the forefront. Edgar Allan Poe said, "It will be found, in fact, that the ingenious are always fanciful, and the truly imaginative never otherwise than analytic."