This contrasts with Class B where (typically a pair of devices operating in push pull each) only operate in the linear region some of the time.
The primary advantage of Class A is that it does not suffer from transient distortion that occurs in class B devices when passing out of the linear region, and for this reason Class A circuits are often preferred for small signal circuits, it being normally the case that linearity (excluding noise) increases as the signal amplitude is decreased. The main disadvantage with class A is that it is not very efficient, a substantial amount of the power drawn by the circuit being wasted as heat (which also increases the size of the designers problem of getting rid of this heat in some cases - high power class A circuits are as much engineering challenges as circuit design problems)
As a comparison, circuits operating in class B, best performance occurs at high power levels (typically just below clipping), but since the distortion products due to leaving the linear region are constant, these become relatively larger as as the signal is made smaller, such that at very small signal levels the distortion levels are very high.
For these reasons most small signal circuits requiring accuracy tend to use class A, whereas high power circuits almost always use class B
Class A circuits are often single ended but a classic application for a pair of class A devices is differential long tail pair, which is exceptionally linear, and forms the basis of many more complex circuits, including many audio amplifiers and almost all op-amps