Diode across inputs to solenoid?

When you put current through an inductor (like the coil in your solenoid), it builds up a magnetic "charge"[*], much like a capacitor stores electric charge. Thus, it resists change to *current* much like a capacitor resists change to *voltage*.

So, you energize the coil by putting a current through it. It builds up its magnetic charge. You disconnect the power, but the coil wants to make the current keep going anyway. You now have a fixed current across a *very* high resistance. V = I x R, so you get a *very* high voltage.

The purpose of that diode is to provide a *low* resistance in that particular direction, so instead of getting a couple hundred volts across your circuitry you get a couple milliamps through the diode. Depending on the circuit powering the coil, different types of diodes (or other devices) might be used for this purpose.

Basically, it "discharges" the coil safely when you disconnect power.

Also, note that contactors have ratings for the coil and separate ratings for the contacts. Make sure you're reading the right ones.