Something is twee if it's a little too cute or overly adorable. A children's book that is sweet and sentimental, illustrated with squirrels in little dresses, could be described as twee.
You could call a flowery hat twee, or describe an elaborate tea party, complete with lacy napkins, fancy silverware, and dressed-up guests, as twee. The word is traditionally British, and its original meaning could have described a dollhouse: "tiny, dainty, or miniature." Much as tummy comes from stomach, twee stems from the (overly adorable) way a child might pronounce the word sweet.