The phrase "making her mouth" refers to the change in the appearance of the mouth. For context the entire sentence was:
Her face had turned a milky yellow colour, making her mouth look redder than ever.
In this case, the author wishes to contrast the changes happening between the character's face and her mouth. The facial color change is the one that causes the mouth to look redder than it actually is. The entire clause "making her mouth look redder than ever" is called a present participle phrase which, in this sentence, acts as an adjective.