"Still I Rise" is told from the perspective of a Black woman who has endured racial prejudice and persecution. The poet, Maya Angelou, was an important proponent of the civil rights movement in the 1960s, and as such, the poem is a defiant assertion of the rights and the strengths of Black people. In the poem, the speaker asserts that she will not allow the aforementioned racist persecution to keep her down.
In the first stanza, the speaker says that no matter how many times she is "trod" upon and beaten down, she will always rise, "like dust." It is impossible to defeat dust, and even the thought of trying to do so is absurd. The implication is that it is as impossible and as absurd to try and defeat the speaker.
The same idea is repeated in the third stanza, where the speaker says that she will always rise up, "Just like moons and like suns." In other words, as the sun and the moon will always rise every day and every night, so will she.
Later in the poem the speaker uses the images of air and water to make the same point. She says that she will always rise "like air," and she also says that she is "a black ocean, leaping and wide, / Welling and swelling." All of this celestial ("as the sun and the moon") and elemental ("dust," "air," "ocean") imagery implies firstly that the speaker can no more be defeated than can the forces of nature, and secondly that the speaker is as fundamental and as powerful as the elements.