To distinguish between the different states of fluid flow one must consider how the fluid reacts to a disturbance in the initial state. These disturbances will relate to the initial properties of the system, such as velocity, pressure, and density. James Clerk Maxwell expressed the qualitative concept of stable and unstable flow nicely when he said:  
That means that for a stable flow, any infinitely small variation, which is considered a disturbance, will not have any noticeable effect on the initial state of the system and will eventually die down in time. For a fluid flow to be considered stable it must be stable with respect to every possible disturbance. This implies that there exists no mode of disturbance for which it is unstable.
On the other hand, for an unstable flow, any variations will have some noticeable effect on the state of the system which would then cause the disturbance to grow in amplitude in such a way that the system progressively departs from the initial state and never returns to it. This means that there is at least one mode of disturbance with respect to which the flow is unstable, and the disturbance will therefore distort the existing force equilibrium.