What does replying a private message mean on here?

A private message is just a message between you and the person sending it. No others see it. People are limited to sending you two messages if you don't respond. Once you have responded they can send you messages without limits unless you block them.

I hope that answers your question and welcome to SW. :)

only you and the person you are writing to can see it

It means that only the person you are talking to can see the thread. It's private so no one else can see it.

It's private. Only you and whoever sent you the message can see it.

Nobody can see your private conversation with the individual.

It’s for private conversations

That you want to chat