How does this Mailing List system work?
Imagine you have some e-mail address. You can send mails to anyone you want. If there are just two people, then things are easy. Alice can send any message to Bob, and he can reply. The whole conversation history is preserved on their machines.
Then, imagine you want to add more and more people into the conversation between Alice and Bob. There are three people, four people, then five, and then it can grow very large. So, what happens then?
In that case, if there are 1000 participants in the whole conversation, then Alice don't want to send the same e-mail to 1000 recipients. It would take a lot of resources, if every member would need to send every message to everyone else. So, what happens then?
Then, people create some mailing list. Which means, all of them send their replies just to a single e-mail address they agree on, and then, this single server is used to collect all of their messages, and to send them to all participants on the list. Also, it makes moderation easier, because if you have "pure P2P e-mail with no mailing list", then Mallory would know the whole list of participants, and could send them some spam. Then, each participant alone would receive it, and would need to manually handle that spam.
So, in the larger communities, mailing lists are useful to manage some conversations via e-mail, between N people. And also, there is usually some kind of moderation, because if you include more and more people, then you need to filter some messages, to keep the whole conversation on a sufficiently high level.
Does person A send an email to person B, with a copy of the Mailing List email?
It can do so. You can write to some person directly, to the mailing list, to both, or to none of them. You, as a sender, can decide, where to send it (you can send e-mails even to yourself-only, if you really want). And then, the recipient can decide, how to accept it. Some people accept only messages from some trusted circle of senders, some others can accept messages from everyone.
This email is then evaluated/moderated and approved or not. And that?
Well, each recipient can deal with its own mailbox, as they please. Which means, you can be a member of some mailing list, but you can arbitrarily decide "I don't want to read messages written by John Doe". Or you can decide that "I don't want to read this topic about Ordinals". This is your choice, and you can just apply it to your message rules, and then it will be handled automatically by your mailbox.
Or are all emails sent to the Mailing List, and then managed by moderation?
Yes, this is also the case. In general, you can just let other people do the moderation, if this is sufficient for you. But you, as a recipient, can accept less messages, if that is your choice.