Domino is the name that describes all the server based processed associated with Notes apps (databases, .nsf files). This includes http(s), access control/user rights management, smtp, agent (code run on schedule) management, search index management, server to server replication, and more.
You can run Notes apps without the server, but as others have indicated, you give up all of the background processes the server provides.
If you're tasked to migrate Notes apps to a new platform and you're not a Notes dev, please save yourself grief and find a consultant who can help. Notes apps can be quite complex and moving the data to another platform doesn't mean you get all the workflow and features present in the native app.
You can run other services on a Domino server, just like you could run other services on an Oracle server, but it's generally advised that you don't; the other services could interfere with some of the Domino stuff and if you try and get help, the various vendors will just blame all the other vendors for the problem; do you self a favor and keep the server clean.
Best of luck.