A waterfall shows time domain distortion due to energy stored in the system being observed across the frequency spectrum. It's a 3D comparable to a windowed sine burst.
The main thing a waterfall can tell you where energy storage occurs with a driver. Metal cone drivers tend to perform best within their intended frequency range, but you'll see their spurious resonances higher up. It can help you design a better crossover by telling you where energy storage occurs and which measures you can use to prevent it, amongst other parameters.
As far as what it can tell you about driver performance, I feel that low energy storage is crucial for transparency and clarity. With the drivers I've had experience with, the best ones for clarity and transparency have always been the ones that had the best performance on a waterfall, CSD plot, or similar.