There are several ways to do this. First, if you right-click or click and hold the terminal icon in the dock, a menu will come up. On that menu, click "New Shell" for a new window. You can also use the same command from the "File" menu. The shortcut for this action is ⌘-N.
This is similar for every app where you can open multiple windows.
You could open multiple instances of an app using the "Fast User Switching" feature.