https://developer.apple.com/library/content/documentation/Miscellaneous/Reference/MobileDeviceManagementProtocolRef/1-Introduction/Introduction.html
"The MDM payload can be placed within a configuration profile (
.mobileconfig
) file distributed using email or a webpage, as part of the final configuration profile delivered by an over-the-air enrollment service, or automatically using the Device Enrollment Program. Only one MDM payload can be installed on a device at any given time."
Sorry to provide such a broad-scope article, but you may want to brush up on what consitutes a device as "managed", and what that means from a management/end-user perspective. When there is an device-level (mobileconfig) MDM profile installed on the device, it then becomes "managed", so to answer your question, a valid MDM profile is an installed mobileconfig profile (System Preferences > Profiles) which designates that device is "managed" by an administrative Mobile Device Management Server (be it an available Profile Manager instance, AirWatch MDM, or any other variety of MDM solutions).
Hope this helps a bit.