A relay operates by using a low voltage/low power (usually) to control a high voltage/high power. The reason for this is that you often don't want sensitive circuit elements responsible for switching power directly. For example, a hot tub on/off switch - The actual switch you turn is a small power circuit used to control the very large power circuit that runs the hot tub. This is to minimize the risk of shocking yourself while using the switch.
In your case your output is 24-240v AC rated to 40A, so that's perfect for your application. You normally want to allow at least a 20% margin on top of your expected max amp load.
Now the input to your relay could be many things. DC or AC at various voltages. A common configuration is DC input 3-20V or so. So you will have to provide 3-20V DC to switch on 110V AC. These two voltages never interact with each other directly, the relay does the talking.
Look for a diagram on how to hook it all up. Google "SSR wiring".
