Command Normals
Command normals are simply moves that require a directional input to be held while inputting the appropriate attack button.
Each character's command normals vary in property and use, but the most common use of command normals is to extend combos and hitconfirms. The combo archetype is to hit with a cancellable normal move, and then cancel that into a command normal, and then finally cancel the command normal into a special or DM. For example, Iori's basic DM combo can be displayed as Close C xx f.A xx qcf,hcb+P.
Strategy Corner
It is possible to cancel from a normal to a command normal in the last few cancelable frames of an attack. This trick lets you retain the uncancelable properties of a command normal, for example, an overhead. This can let you pull out some overheads out of nowhere, when an enemy isn't expecting them!