Drive by wire is a term derived from the aeronautic term "fly by wire". It indicates that some portion of a car or other land-going automobile is not controlled by direct mechanical means, or at least not entirely controlled by direct mechanical means.
The most common use of drive by wire is "intelligent" throttle control; The car's ECU determines your current speed, RPMs, and gear, as well as the pedal position and the rate of pedal travel, then makes a decision as to how much air and fuel to deliver based on what it knows of its own performance in order to be as responsive and efficient as possible.
Some production vehicles are even making use of drive-by-wire power steering with no connection between the steering wheel and the front wheels which do the steering. This necessitates the use of force feedback to let the driver know what the car is trying to do.
It is arguable that the use of electronically-controlled transmissions (both automatics, such as the tiptronic used in BMW and Audi automobiles, and electronically-clutched and shifted "manual" transmissions such as that in the Ferrari F355 F1) could be considered drive-by-wire, but the term is usually reserved for electronic simulations of traditional motions. Hence it would clearly apply to steering or depressing a throttle, but perhaps not pressing a button in lieu of moving a shift lever.
Many gasoline hybrid vehicles use a completely drive by wire method to control throttle because they in fact do all of their starting acceleration with electric motors, and only activate their gasoline (or diesel fuel) engine when they are already up to a certain level of speed. The Ford Escape and the Toyota Prius fall into this category, while the Honda Insight does not.