Media will only appear in the Media Library if it has been uploaded through the Upload menu and the user has permission to view content in the area where the media was published.
The Media Library respects area security permissions, so users may see different media depending on their level of access. For example, if a user cannot view content in the Human Resources area, they will not see media published there.
Media uploaded directly through the media picker while creating content is personal to the user who uploaded it and will not be visible to others.
To make media available to all users, upload it through the Upload menu and publish it to an area that everyone can access.