Celestial Steed summons a Celestial Steed, which serves both as a flying mount in Outland and Northrend, and a ground mount in Azeroth.
Though the mount is adjusted to your riding skill and location, it only does so when you mount up. For instance, if you mount up in Dalaran, you will have a non-flying mount. If you then ride into Krasus' Landing it will not automatically turn into a flying mount. To fly, you will need to dismount and mount up again.