If you give a loud shout in a cavernous place, like a gym or a church, the sound of your voice will reverberate throughout the room. Reverberate means sound waves traveling back and forth, as in an echo.
Often we use reverberate to talk about sound, or sometimes light. If a noise echoes for a long time, we can say the space reverberates with that noise. You may have heard of a reverb effect in audio processing, which is basically a long echo. We also use the word metaphorically to describe the impact of huge events. For example, the 2008 mortgage crisis in the US reverberated throughout the world’s economy, causing a global recession.