Part of that general role involved managing monetary systems in a way that would reduce the risk of panic and instability in the first place. But it also meant applying Bagehot's famous principle that central banks should lend freely, at a penalty rate and on good collateral, in the event that a crisis occurred.
The liquidity management role of central banks also led naturally to their engagement in other areas of financial stability policy, including exercising a degree of oversight of the banks that they were lending to. Obviously the world now is very different from what it was in Bagehot's day.