(Photograph courtesy of Wikipedia - Image is in the public domain.)
The door zone refers to the area at the side of parallel parked cars and trucks which would be intruded upon by the car door, were it to be opened. The door zone is hazardous for cyclists to ride in, since a car door often opens without warning, leaving the cyclist no opportunity to stop in time to avoid it. Bike lanes sometimes have portions that overlap the door zone. If such were the case, it would be extra hazardous for the cyclist to swerve into the car lane in order to avoid a collision, since any passing traffic would not be expecting such a maneuver. If there were no bike lane, there still may not be the expectation of such a maneuver. Worst of all is the case where the opening car door directly knocks the cyclist into passing traffic; fatalities due to such have occurred.
This old list of car widths with the driver's side door fully open, courtesy of John S. Allen, illustrates the wide range of widths of vehicles. He assumes that the vehicles are properly parked, with 6 in from the curb to the right tires. An examination of this list shows that for the widest vehicle, even when parked near-ideally, the vehicle and door spans a width of almost 10.5 ft. Typical vehicles span 9.5 ft or so.
The reason why I term the door zone "infamous" is that it appears that tremendous amounts of resources are required to eliminate the danger of dooring for a bike lane placed adjacent to parallel parking. If 7 ft (the AASHTO minimum) is allocated to mark the parking space, a whole 4 additional feet would be needed to guarantee that a large, properly parked vehicle won't intrude upon the door zone. Four feet is the minimum width of a standard bike lane, when no curb is present! Furthermore, not all parallel parked vehicles are parked perfectly. (In San Francisco there are experimental T-shaped road markings for parallel parking that give people clues on how well parked vehicles are.) Such space is seldom available in practice; hence frequently there is vigorous debate over the safety of combining bike lanes and parallel parking. Cyclists can mitigate the danger by being alert and watching for poorly parked vehicles. They should always ride outside the door zone. If necessary, they can ride outside any bike lane to remain safe. Often, riding in the left half of any bike lane is enough to avoid problems, since bicycles are usually around 1.5-2 ft wide. There are other experimental proposals. One places the bike lane arrows on the left side of bike lanes. Another is having a hatched buffer between parked cars and bike lanes. Finally, drivers and car passengers can be trained to watch for bikes before opening their doors, as they are in Europe. As good as these ideas are, none of them solve the problem without still requiring tremendous road space, which is why the door zone is infamous.