What does the phrase 'hearing crickets' mean?

If the speaker pauses, expecting a reaction from the audience such as a laugh or applause, but the audience is silent (maybe it was a very unfunny joke the comedian just told), then the room may "hear crickets". Additionally, it can refer to two people debating. If one debater gets a strong point across and the other has no response to it, the audience may "hear crickets".

In the countryside, at nighttime throughout much of the year, you can hear actual crickets (the insects) chirping, because there is not a lot of extra noise. In cities, there’s often too much ambient noise, from cars driving by to people listening to music, from construction to the noise of appliances running, to hear the crickets. But occasionally, things will align such that there is a relative silence for a moment, and you can hear the crickets chirping.

It’s not that they only chirp when there’s silence: they chirp all the time, but you can only hear them when it’s quiet. A related phrase is "hear a pin drop". If you’ve ever dropped a pin (a little straight pin, not a pushpin or thumbtack), you know that it makes very little noise.

Thus, if it is "so quiet you can hear a pin drop", you know that it is very quiet at the moment.