I believe that they provide liquidity. That’s a fancy way of saying that they ensure that any time someone wants to sell he can find a buyer, and every time someone wants to buy he can find a seller. That in turn means that folks are more confident of their ability to enter and exit a position, which means that they are more likely to enter and exit positions, which makes the market more efficient at finding prices.

And of course prices are hugely valuable: the market is a conversation about the relative value of everything, and the language it speaks is prices. So by enabling liquidity, high-frequency traders are enabling efficient allocation of resources towards those things which mankind most dearly needs and desires.