It's an Amazonomachy, or a mythological battle between the Greeks (almost certainly the Athenians) and the Amazons. In black figure vase paintings, men are conventionally shown with skin painted black, women painted white. There are no other contexts where you'd see women armed and in combat, and the Amazonomachy is a common theme. Herakles isn't present, hence my suggestion that it's the Athenians. Here's another couple examples of the same theme: 1, 2.

The figures aren't labeled so it's hard to be more specific without any contextual information (where is this vase held? what is its catalog number? where was it found?).

It's been far too long since I've had any practice dating vases, so I can't pin it to the correct decade like some people can. For what it's worth, I'd say it looks like it's Attic, second half of 6th century BCE. Take this last bit with a pinch of salt though.