When are two waves said to be 'coherent'? What does that imply in terms of their Phase difference?Amplitudes?Path difference?

Wave coherence occurs when two or more wave sources
generate waves at the same time, having the same frequency, amplitude, and phase.
 Coherent waves can also be described as "synchronous." The frequency is the rate at
which a vibration occurs, the amplitude is the maximum extent of that vibration, and the
phase refers to the degree of synchronicity between the vibrations.  Waves are
considered incoherent or asynchronous if they have no stable phase relationship between
them. Path difference describes whether waves will tend to interfere with each other
constructively or destructively.   See more at the link for an animated
demonstration: