DMZ is short for: DeMilitarized Zone. It's an area/lan/subnet of your network that is neither extremely secure (inside) nor extremely open (outside) to the public. It's something in between. Take for example a web server, the outside/internet users are allowed to view the web pages on the web server. However, the outside users are not allowed to do any thing else with the web server, such as pinging it or connecting to it using remote desktop. So the web server need to be put in DMZ, and configure the firewall to allow web (http) traffic to flow to the web server.
Here is an example for configuring DMZ on an ASA firewall: