Very many automatic car users are careless to understand the gearing transmission system of autos. We are aware of 'P, R, N, D, D1, D2, D3' or 'P, R, N, A, 2, 3, L' in our cars and we understand only P=park, R=reverse, N=neutral and D=drive only. The others' function are discussed bellow.
The d1, d2, d3 can be used for engine braking. That is u can use it to downshift when u are going down the hill or nearing a red light and u don't won't to use ur brakes, just like in manual. If u are moving say in gear 4 and u shift to d2, ur car will downshift to gear 2, likewise ur car will downshift to gear 1 if u shift to d1. This is useful in slowing down the car in case of brake failure.
For D1, when u're stucked in sand or mud and u need to maintain gear 1 power to get ur car out.
For D2, when u're ascending a hilly road and ur engine is loosing power. To gain instant engine power, u need drop to D2( just like in manual trans)
For D3 (if a car does not have it, OD button does the function), when u're trying to overtake in low rev say 2500 rpm and need to rev up to say 5500 rpm to gain more engine power to overtake successfully.
Also 'D2' 'D3' functions are designed for emergency scenario, a situation where your gear in 'D' could not change itself automatically due to electrical or mechanical malfunctioning, all you need to do is to drive the car manually and it has no side effect of on your car.
Some automatic cars dont have such d1, d2, rather they have +/- .The plus shifts up while minus down shifts the gear. Some like mercedes have it also behind the steerin like paddles. Mercedes C-class, ML and Volks passat cars, never upshift or downshift except in extreme cases of engine revolution above or below safety limit. It makes the experience similar to driving a manual car without the third pedal
Unlike the manual, you can change gears to upshift or downshift as asserted without having to hit on your brake pedals at such extremes of speeding by suppressing the knob on the head of the gear shift selector handle to pick on the specified gear you wish to be on. So for automatic, if I'm moving at, say 120km/hr on 'D', I can just change to, say 'D2' without stepping on the brakes, and the car will slow down automatically?
A professional drivers use this to control when they want their cars to shift to lower or higher gears at the right rpm. A professional driver who knows how to handle auto gears will outrun an ordinary driver even when they are both driving the same cars with the same auto tranny. If u watch fast and furious 6, most of the cars they used are automatic but the drivers controlled when they want the cars to shift.