A frame of reference with respect to which an object with no real forces acting on it will move with constant velocity, i.e. no acceleration. Newton's Second Law applies only in inertial reference frames. This definition assures that F=ma will apply in an inertial reference frame. In fact, the first law may be regarded as a special case of F=ma in which F is zero, and hence a must be zero. It deliberately excludes accelerating reference frames such as a car going around a level turn - in this reference frame there are fictitious forces that appear to be acting on all masses, pushing them away from the center of the turn (centrifugal forces).
An inertial coordinate system has no acceleration with respect to objects with no measurable force on them. Although its acceleration is zero, its velocity can have any arbitrary value. Hence any frame of reference moving with constant velocity relative to an inertial reference frame is also an inertial reference frame.