It's an "eye cup" with a satyr - a mythological creature that's part man and part horse - pursuing a maenad - a female follower of Dionysus. He's easily identifiable by the ears and tail, the female is less clear, but these kind of scenes are pretty popular (so she's identifiable by the similarities in iconography) and she appears to be wearing an animal skin over her skirt. Usually maenads carry a staff topped with a pinecone called a thyrsus, but the scene here is pretty compressed.

Figures of satyrs and maenads are pretty common on drinking cups as both of these figures are devotees of Dionysus, the god of wine. It's not clear whether they were just meant to be entertaining/eroticized images or warning against the ridiculousness of excess. It's possible that they are ambiguous enough that whether the scenes were admonition or encouragement is up to the viewer.

On a side note, the big eyes on this particular cup are part of the humor of ancient drinking parties. It acts as a sort of mask. This example is really too steep an angle for how you would actually drink from the cup, but it makes the point.