I just started using MongoDB and Node.js with a MEAN Stack (MongoDB, Express, AngularJS, Node.js) on my local machine and at first I assumed that MongoDB was installed on the Node.js server kind of like MySQL is installed on Apache when you install the LAMP or WAMP stack.
But now I'm not so sure any more :)
How does it work? Where is MongoDB installed? Can I use it without Node.js? Can I use MySQL without a server?
Both MongoDB and MySQL are installed standalone on the host (in your case localhost).
MySQL is not installed on Apache. It's just the PHP interface to MySQL which requires Apache to serve it. You can use the MySQL command line (issue the mysql command in your shell console) without having Apache or PHP installed. The LAMP and WAMP stacks ship with the PHP MySQL interface configured.
MEAN is a similar stack, consisting of each individual component available independently as well as knit together seamlessly as per requirement. You can query a MongoDB hosted on a different machine from the machine you have the MEAN stack on too.