Two light sources are said to be coherent if they maintain a constant phase difference over time. This means the waves emitted by these sources oscillate in step with each other, usually having the same frequency and a fixed phase relationship.
Coherence is essential for producing a stable and visible interference pattern because fluctuating phase differences would cause the pattern to blur or disappear.
Therefore, coherent sources have:
\[
\text{Constant phase difference} \quad \Rightarrow \quad \text{Stable interference fringes}.
\]