The My Sites menu item lists all the sites for which a user is an administrator. If you have a different user level on another site in the network, it will not be listed.
A drop-down at the top of the page refers to the user's Primary site. This is used as an identifier for when a user logs in. It allows access to the backend of the primary site on the user's network.
Each site is listed in the order they are created. Below the name there are links to the front end and admin area of each site.
Once a user finishes all admin duties, they simply click the blue button "Save Changes" and all of their additions to their site will take effect.