A compressor map shows the operating range of a compressor and how well it works within its operating range. Two fundamental requirements for the gas flowing through a compressor explain why it works best at a design condition and not so well at other conditions, known as off-design. First, the exit area has to be smaller than the inlet area because the compressed gas has a higher density. The exit area is sized to pass the specific volume at the design condition. Second, all the rotor and stator blades in an axial compressor, and impeller inducer and diffuser vanes in a centrifugal compressor, are angled to meet approaching air head-on at the design condition to minimize incidence losses. Incidence losses reduce the efficiency of compression. Satisfactory operation of the compressor relies on controlling the angle at which the gas approaches rotating and stationary blades to within an acceptable range. Deviating from the optimum first results in increased losses/reduced efficiency then either stalling or sonic velocity/choking which occur in the blade passages at opposite ends of an axial compressor at the same time. They also occur in a centrifugal compressor at entry to the impeller and in the diffuser.
The compressor design point will be in an area of high efficiency whether the compressor is part of a gas turbine engine or whether it is used for pumping air into a blast furnace. However the compressor has to provide suitable performance at other operating conditions imposed on it which means a high efficiency is required over a wider range of operation. In the case of a gas turbine engine it must permit the engine to be started readily and accelerated rapidly to the design speed which means operating at lower speeds than the design speed. At speeds and flows away from the design point the compressor flow area reduction is not appropriate for the actual density rise. A NACA report illustrates pictorially the difference in contraction required at the design condition and at low speed. At lower speeds, for example, the gas hasn't been compressed enough to exit the compressor without adversely affecting the blade angles of attack through the compressor.  Away from the design point the middle stages of an axial compressor continue to operate at about the optimum angle of attack but the front stages deviate one way, towards stall, and the rear stages in the opposite direction towards choke. The deviation was acceptable up to a design pressure ratio of about 5:1, producing only a loss in efficiency. At higher design pressure ratios prevention of rotating stall, which occurs at low corrected speeds, and choking was required with the introduction of inlet guide vanes which partially closed at low speeds, or by removing air part-way along the compressor at low speeds. Rows of variable stators or split compressors, which allowed the front stages to speed up and the rear to slow down relative to each other, would also be introduced for the same reason. When pressure ratios reached about 12:1 compressors would incorporate more than one of these features together.