My Honda Civic has a D gear and a D3, which apparently prevents it from going into 4th. Why would I want to do this? What is it good for? Does it make my fuel efficiency better or worse? Does it make the transmission's job easier or wear it out faster?
This is analagous to down shifting in a manual. This is a lower gear for the transmission which means the engine revolves at a higher rate producing more back pressure at the same speed as a higher gear.
When going down a hill, if you downshift that will reduce the demands on the braking system, due to the back pressure. You will often see truck drivers downshifting on long hills so that their brakes do not overheat.
You would only use D3 while going downhill with a load so you can use your brakes less. Your mileage would be worse since the engine is running at a higher rpm. Only if you did a lot of using D3 would it make any appreciable wear on your transmission.
In addition to what Patrick said, D3, or whatever else it's called in various makes and models, is also useful for those times when you're climbing a hill and the transmission keeps shifting back and forth between gears.
There may also be times, such as when driving on very slippery surfaces, when a gear shift could cause the car to lose traction. In such a situation the ability to hold the car in a given gear can be very advantageous.
Personally I use D3 in and around town, in built up areas (<50km/h or 30 mph) there is no need for D4. Use D4 on the open road (motorway/freeway) for speeds above 60km/h (>40 mph). Also use D3 for towing and hill climbing/descending for better engine braking and avoiding constant shifting between D3 and top. Worked mint for me (still very economical) and I have owned 3 Accords :D
Drive (D3) - This position is similar to D4, except only the first three gears are selected. Use D3 to provide engine braking when going down a steep hill. D3 can also keep the transmission from cycling between third and fourth gears in stop-and-go driving. For faster acceleration when in D3 or D4, you can get the transmission to automatically downshift by pushing the accelerator pedal to the floor. The transmission will shift down one or two gears, depending on your speed.
This is quoted from the Honda Civic owner's manual.
I think using D3 in areas that are signed 40MPH or less eliminates a lot of shift changes between the various higher speeds on your transmission. If the road is signed 40 MPH and under, I always use the D3 button. I also use it if there is ice or snow on the roadway, but the main thing is the wear and tear on a transmission trying to go up a hill or around a curve in a very high gear which is hard on engine and transmission.