They also call it “Present Progressive”. The name itself already tells us that we use it when an action is taking place in the present “right now.” should be understood here as:
Moment of speech in the present
Time axis 1. Pay attention to the red circle that says “right now.”
We can understand “at the moment of speech” as “right now” in the present:
now, at this very moment, at this time, right now (note: all these examples in other contexts may not necessarily mean moment of speech. But for the purpose of this lesson we are not talking about it)
At this very moment, thousands of people are watching the match!
While we are talking here, thousands of people are watching this match!
We can explain “moment of speech” if we use an example. Imagine you are talking with your friend. Your mom is cooking dinner. You say:
Please stay with us, my mom is cooking dinner!
When you are physically saying it, at this very moment of your speech, your mom is really cooking. That is why we call it “moment of speech”, and we use Present Continuous (is cooking), if the action is happening at the moment of speech.
Moment of speech is basically moment of speaking. So, Present Continuous is used for actions that are happening at the moment of speaking.