The story behind painting is that the centaur is a lustful creature and is always trying to tame his desires. Pallas Athene (Hence the title) is the goddess of wisdom, and begins to tame the centaur from his beastly instincts.

Botticelli painted this work because he was making a wedding gift for a couple in which the man was famous for his lustfulness. The metaphor basically tells the couple that the woman in the marriage must control her husband and 'teach him to behave'.

This information and more on this painting can be found at the link below.