What exactly is steamworks?

It apparently provides a lobby service and voice chat, with integration ito steam.

Does steamworks host our servers for us?

It mentions anti-cheat and anti-piracy.

I’m very confused what it is and what it is not, it seems to be a huge grab-bag of ‘stuff’

Basically it is. It’s the SDK (software development kit) for integrating with a bunch of steam services which include what you mention. It doesn’t do server hosting but does do the matchmaking to the servers you host.