The diode is there to suppress a high voltage spike that occurs when the coil for the solenoid is released. It drains that shock to ground instead of into your circuit. It is pretty much a must have on solenoids and a recommended practice on relays.
Normally when you hook up a solenoid it doesn't matter which terminal you hook your signal wire to, power to 86 and ground to 85, or vise versa, however because this has a diode it makes the solenoid polarity sensitive, in the sense that you must put power on the cathode side of the diode otherwise you would have a direct path to ground.
However, looking at this solenoid, it looks like it has a Zener diode going both ways (which honestly I have never seen before and we see ALOT of stuff go through our shop) and that to me makes it non-polarity sensitive again, while still giving the benefits and protection of a diode suppressed coil.
That being said, no matter what, you should diode suppress any solenoid you put in if it doesn't come with it. That shock can damage leds, solid state switches, etc. we had all sort of problems with a truck that had a tank level gauge on it. Every time we turned the truck on and off we would blow out and led on the gauge. We replaced that gauge 3 times before we finally found an unsuppressed solenoid that was causing the issue. Took a .03 diode, stuck it between 86 and 85, and no more blowing out the tank level gauge.