Traditionally, Carinatae were defined as all birds having a keeled sternum. The carina or "keel" referred to a strong median ridge running down the length of the sternum, or breast bone. This is an important area for the attachment of flight muscles. Thus, all flying birds have a pronounced carina. Ratites, all of whom are flightless, lack a strong carina. Thus, living birds were divided into carinates and ratites. The difficulty with this scheme was that there have been (and still are) any number of flightless birds, without strong carinae, but which are descended directly from ordinary flying birds with carinae. Examples include the turkey, a galliform (chicken-like) bird, and the dodo, a columbiform (the pigeon family). None of these birds are ratites. Thus, this supposedly distinctive feature was easy to use, but had nothing to do with actual phylogenic relationship.
Unfortunately, the use of this term to describe the Ichthyornis-Neornithine group turned out to be equally inapt. Various dinosaurs -- apparently, remote ancestors and cousins of the Carinatae -- do possess a keeled sternum. So, evidently the presence of this structure does not necessarily imply its use in flight. This sort of definitional problem is one reason why the use of physical characteristics to define or name taxonomic groups is now discouraged.
The characteristics that actually are unique to the Carinatae have little to do with the sternum. Rather, carinates are unique in having, for example, a globe-shaped, convex head on the humerus and fully fused bones in the lower leg and outer arm.