Breaking down means that the diminishing abrasives in a polish reach their final, extremely fine state, and they practically disappear. Their size is getting smaller and smaller, and after they performed the initial cut (while being in their original size), they break down into finer particles and do the final fine polishing of the surface, giving high gloss and great clarity. Heavier products, such as compounds usually contain macro abrasives (gritty feel between fingers), while other types, such as finer polishes contain micro abrasives (lotion-like). The abrasives (grit) are 'agglomerates' which break down to smaller, finer particles 'primary crystals' as they work. This can happen mechanically and/or temp-sensitively.
As you watch the trace of the polish, you can see that it gets finer as you progress with the procedure. When the polish is so fine that it is almost translucent, opaque - because the particles in it are now ever soooo small - this is the final state of its working cycle - the polish has broken down, and it is ready for removal.
Don't work them until they start to dust because dust particles can mar the finish. In the end, you will end up with less residue, easier removal. There is no firm timeframe for the working time of a given polish. Count in factors like outside temp., surface temp., humidity, pad type, pressure, machine speed, etc. Flashing means that a polish reaches an unwanted dry state very suddenly, often without completing its working cycle.