I'm not a conveyancer, but I've bought a few properties and have watched the process more than once. Bit like watching paint dry, really.
They do the title searches etc and ensure there are no issues with cavets etc.
They also need to gather information regarding outstanding monies and monie alreayd paid by the vendor for things like council rates, body corporate etc etc so they can be apportioned on settlement day.
I think the conveyancers usually book the settlement between each other once they get the go ahead from the financial institutions involved and their solicitors.
I've been to where they do the settlements. Once. Bizzaro world. A bunch of people running around with mountains of docs, bank cheques etc shouting each others names. It's like something out of Discovery Channel, except they're not looking for a mate but the conveyancer for the other side of the transaction. It looks very frantic and chaotic, but they seem to get the job done.