You run each hot leg into the line side of the contactor, and out the load side of the contactor. The coil operates at 120v, so you run one hot to it, and the neutral to the other side. Since it is a normally open contactor, when the coil is not energized, no power runs from line side to load side. When the coil is energized, the circuit closes and power runs from line side to load side for both hot legs.
You control the power to the coil with a switch. I suspect the 63a contactor is for your "main power" switch, and the 25a contactor is for an element switch. When main power switch is off, you have no power from the load side of the 63a contactor to the rest of your panel. When the element switch is off, you have no power from the load side of the 25a contactor to your element.