I don’t remember the first time I was told about the power of silence in conversation, but I’m pretty sure it was one of my first management classes. I’ve run into the concept both formally and informally many times since then, and the usual context is somewhat adversarial.
For example, when performing a job interview, if you aren’t that impressed with an answer, wait a few beats. Does the candidate fill the silence? Do they elaborate? And does their answer dig a deeper hole or do they begin to climb out? You can learn a lot with this technique: someone who immediately realizes the impact of their words and tries to work the conversation back in the right direction is showing a great deal of emotional intelligence. Someone who manages the same feat but only after being prompted and guided is in a different place (this may not be a bad thing; it depends on what you’re looking for).