The personification in the first stanza reveals that the speaker feels alienated from her own body. Personification occurs when a writer attributes human characteristics to an inanimate or non-human object.

The line that uses personification is "my skin has betrayed me." Of course, only a human can betray another human being, but the speaker feels that her skin—her outward covering or exterior—has somehow let her down. This could refer to her being black in a racist society, or it could refer more generally to a feeling that how she appears on the outside doesn't reflect who she is on the inside, a common emotion during adolescence.

The poem is generally about the revolving and repeating worries and anxieties experienced by a 14-year-old girl dealing with all the changes that come as one grows into adulthood.

When the poet says, “my skin has betrayed me,” she is attributing human characteristic to her skin—as if her skin had its own brain, and for some reason it had decided to betray her.

Audre Lorde was a black Caribbean-American writer known for her concerns over the marginalization of black women and the injustices of racism and sexism.

When Lorde mentions the word “skin”, it seems natural to suppose the girl must have experienced different behavior because of the color of her skin. In subsequent lines, we hear the girl say disappointedly that a boy was chosen over her "on Math Team" despite her better performance. She says,  

“I should have been on Math Team   
my marks were better than his" 

So we see that the girl is merely fourteen years old, yet she is able to feel the evil influence of racism on her life. She is learning that the society is biased towards people of color, and that she, too, is a person of color. Therefore, she says, "...my skin has betrayed me."