I notice women do it a lot more then men do,they also do it surprised as well.
I have always wondered this as well thanks for asking this.

To hold down the puke.

To hide your shocked expression.

Because we are mostly creatures who mimic others and it is now ingrained into our culture. I suspect it was once considered polite.

So we don’t swallow a bug while gasping?

I’m sure my grandpa would say so the flies don’t fly in.

It is considered impolite to offer any of our orifices open for viewing.
As it is sometimes difficult to keep our mouths closed during certain moments, such as amusement or horror, decent persons would have used fan, hanky, or hand to cover the gaping hole. Then, as already offered above, over time it became mimicked behavior.

^^^ I will buy that.

By the way, I’m watching My Fair Lady right now, and there is quite a lot of this very thing taking place when she shouts, “C’mon Dovuh, move yer bloomin’ ass!”

It is a learned reaction.
For example, in some parts of Asia, people stick out their tongues when surprised.

Hence the word gobsmacked

I have noticed that many women and some men cover their mouths when broadly smiling or laughing.

I don’t know if it’s really learned or almost an instinct. I guess I’ll watch more closely.

@Bill1939 I think people who are self conscious about their teeth do that.

Maybe to block evil spirits from diving down your throat?