To be somewhat silly or goofy, while still having a certian amount of sophistication; sort of like having a mellowly comical behavior. If you think of the humorous frivolity of silly inventions, such as the works of Rube Goldberg, you have discovered the essence of 'whimsical'.

I found the other definitions here lacking in depth and only giving synonyms or a very brief sentence. If you look at the context it is frequently used in, the word 'whimsical' doesn't really have any direct synonyms. It has a meaning all it's own.