This is the 1892nd most frequent Chinese word.
可爱
Cute; lovable.
In this sentence, '可爱' is used as an adjective to describe the appealingness or charm of the puppy.
这个小狗很可爱。
This puppy is very cute.
Here, '可爱的' is used as an adjective modifying '微笑,' indicating the pleasant and charming quality of her smile which impacts emotions.
她可爱的微笑让人感到温暖。
Her lovely smile makes people feel warm.
'可爱' is again an adjective describing the attraction or endearing aspect of the anime character.