Sometimes I find the word “creature” to describe a person like “She is a little lovable creature.” I am always confused because I feel that this word is mainly used for animals. In what situation the word “creature” is preferred to describe a person?
Yes, creature is mainly used for animals. Occasionally, it can be used metaphorically to refer to people. In this case, it implies a foreignness or strangeness.
In the phrase, "She is a loveable little creature", I think that the speaker is implying that "she" is a little odd, in an endearing way.
However, it is not always positive: sentences like "I can't believe he did that. What an awful creature." are also acceptable. Here, the nuance of strangeness or foreignness is used to imply that "he" is almost subhuman. While it can be positive or negative, calling a human a "creature" will always (in my opinion) imply strangeness, quirkiness, or difference.
Another definition of creature but not implying strangeness or animal tendencies: "One who owes his position to another; one who is actuated by the will of another; an instrument or puppet"(SOED). The example of that usage quoted by that dictionary is obviously old:"Sir Francis Windebank ...was a creature of Laud's house".