The drive mode switch is on every Q50. All hybrids, and any gasser with Deluxe Touring have Direct Adaptive Steering (Steer by wire). Those cars can therefore allow personalization of settings. Personal Mode is just that, personalized. You go to the Drive Mode settings app and customize it. You can set whether the transmission is in standard or sport mode - sport raises the shift points so the car up- and down-shifts at higher rpm's. You can choose how "heavy" the steering wheel feels and also how responsive the steering is. You can also turn on or off Active Trace Control. ATC is a feature on many Infinitis that uses braking of the two inside wheels on a turn to help the car almost 'pivot' around a corner - basically it just makes cornering feel better.
Snow mode - retards throttle response, especially at low speeds. Helps minimize wheel spin when starting in slick conditions. For those of you who grew up driving manual cars in snow, I equate this to starting a car in second gear.
Eco mode - for cars equipped with the Eco pedal, will give a little force-feedback in the gas pedal to basically remind you that the pedal on the right is the one that costs you money. Eco mode will also keep the tranny in standard mode - and I'm not sure, but may make efforts to keep rpms down whenever possible.
Standard - your car will always start up in Standard mode. This seems to be a middle of the road setting. Standard transmission performance, medium 'weight' of the wheel and medium steering response.
Sport - tight, heavy wheel feel and sport transmission setting. As stated above, none of the settings, including sport, affect suspension at all. If your car has an S on the trunk, you have sport suspension. If it doesn't, you have normal suspension.
Personal - see above. Play with the settings to your heart's content.