as above @dexter_kane is on the money.
As to terminology…
a DMZ is from military terminology (probably specifically korea) - De-militarised zone. North and South Korea have stretch of land between them called the DMZ, which is basically like no man’s land between the two countries.
Basically network-wise, its a place (VLAN or different physical switch) behind your firewall that is somewhat protected from the internet, but allows specific traffic through to hardened edge servers that you want to have outside your protected network (but not directly on the internet).
its a halfway house, if you will for semi-trusted machines that you want outside of your “inside” network in case they get hacked. Anything in the DMZ should be hardened as much you are capable of, as these machines are still partially exposed to the internet. anything in the DMZ should also not be a server that permanently stores any sort of data (in the case of a mail relay, it is store and forward to the internal server, only in flight data sits on it while it is being processed).
so, things like domain controllers, etc. do not belong there. they’re too vulnerable and not hardened. they permanently store large amounts of private information that you don’t want to be stolen.
think: hardened DNS servers, hardened mail relay servers, reverse web proxies, malware scanning proxy servers, etc. all those sorts of things belong in your DMZ. The idea is that even if these machines get hacked via some protocol exploit for the service they host, they have limited ability to get back into the fully protected “inside” network to act as a launchpad to hack that.
Active directory, mailbox servers, etc. should be on your inside network, either on the same network as your clients or ideally (if you can afford the complexity) on a server network that is protected somewhat from your users (modern stance is that even inside network users are untrustworthy bastards who may either get hacked (web exploit, home internet connection, internet cafe, etc.) or try to hack your stuff themselves).