Is this a trap?(!)
As a non-scientist, I'd have to say only in the most basic way (and you might disagree even with that). Here's my understanding:
On a classical level, two waves (e.g. water waves) are coherent if they propagate through the water with the same frequency, amplitude, and time phase. Two such waves generated from the same point in spacetime will act as one wave with twice the amplitude. They interfere constructively rather than destructively. (I also know there are different kinds of classical coherence - spatial, temporal, spectral, etc. - but I'm not interested in that.)
On a quantum level, wave properties are defined by their wavefunctions, which indicate the probability of different variables under different constraints. Quantum coherence, as I understand it, means two or more particles, say electrons, that are in-phase, and can be defined by a single wavefunction. (I don't really have a clear visual sense of what that means though; if you can give me one, I'd appreciate it much.) Macroscopic quantum coherence leads to special phenomena like laser light, superconductivity, and superfluidity. Like classical waves, quantum waves constructively interfere, increasing each other's strength.
I'm not sure if that's all exactly right, but where I'm less clear is about how quantum wave-particle duality fits in with coherence. I understand coherence in terms of waves; what I want to know is whether it's equally valid to speak in terms of particle coherence, and if so, how to describe it (in simple lay terms). (I know that in QM you can't really distinguish between particle and wave, because everything is both, but I wonder if there's any validity at all to describing it in physical terms to a general audience that can't as easily grasp the wave side of it.)
