What means linear response for accelerometers?

What means that accelerometers measures linear acceleration and, in particular, that they are a linear response?

• In General - The real time values what you get from sensors, plot them in a graph and connect the data points. If you get almost a straight line, it means your getting a linear response and your readings are consistent. If there is too much deviations, then it means your system is unstable. And, sometimes to get linear curve or better response, the existing data points are used to compute interpolated data points using linear or polynomial equations. – PsychedGuy Feb 5 '16 at 17:12

The second use, in "they [have a] linear response," means that the output of the accelerometer is directly proportional to the physical acceleration, like $V_{out} = C_1\cdot a + C_0$ where $C_1$ and $C_0$ are constants. The response can only be linear over a certain range of accelerations because there are limits on the output voltage, etc.