We know that sound consists of vibrations in the air or other medium transmitting it and that it causes objects on which the waves impinge to also vibrate, even if we cannot see it with the naked eye. But in theory at least, by closely observing the vibrations of the object, you should be able to reconstruct the sound that caused it to vibrate.
It turns out that you can now do it is practice and it is the great sensitivity of modern instrumentation that enables us to do it. Researchers from MIT, Adobe, and Microsoft played music to plants while taking high-speed video. Then using sophisticated algorithms, they were able to reconstruct from the silent video of the plants a pretty good reproduction of original sound. They repeated the exercise with someone speaking near a bag of potato chips in a sealed room with soundproof glass while taking the video through the glass, and you can actually make out the words.
One obvious application of this is for espionage, to figure out what people are saying from video even when you are not close enough to hear.
But there are many possible uses. A more interesting (to me, at least) is that we may be able to reconstruct sound from old silent video. Of course, the researchers were able to use high quality, high frequency video for their work, not grainy old footage. But they were able to get some results using regular video cameras as well and as the sensitivity of the detectors increase, it may become feasible to figure out, for example, if the actors in silent films were actually saying what the subtitles say.