The acceleration of a body is defined as the rate of change of velocity. If v is the velocity of a body and t denotes time, then acceleration, a, of a body can be written as:

a = dv/dt

When acceleration is zero (that is, a = dv/dt = 0), rate of change of velocity is zero. That is, acceleration is zero when the velocity of the object is constant. 

Motion graphs represent the variations in distance, velocity and acceleration with time. For zero acceleration, the distance-time plot will be a line of constant slope (v = dx/dt, that is velocity is constant). The velocity-time plot will be a straight, horizontal line (depicting a constant velocity) for zero acceleration. The acceleration-time plot will be a straight line coinciding with the x-axis, since acceleration is zero.

Hope this helps.