This looks like a mechanical sprinkler controller, which I’ve never seen to be honest. My guess is that the 240V AC output is connected to a pump. I am curios how many zones do you have? The only manual I can find is this one:
http://lib.store.yahoo.net/lib/kingpumps/LEG-CTL-R88169101C-Intermatic-Manual.pdf
which doesn’t tell much.
Most sprinkler solenoid these days work with 24V AC (note: NOT 240V AC!). That’s also what most sprinkler controllers work with. If you have a 240V AC pump, you can use a ‘pump start relay’, which you can think of as a sprinkler solenoid, except it’s used to switch a 240V AC pump.
To understand your situation: how many zones do you have? Do you have a pump?