Command Normals
Command normals are moves that require a simple directional input along with 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 cancelable 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 > f+A xx qcf hcb+P.
For some characters, the classification of their moves can be counter-intuitive. For example, Chin's Nikikyaku (df+B) has an input which is typical of command normals; however, it is actually a special move. Chin's Choukarou (d d+K) and Zabantetsu (d d+P) stances, on the other hand, are actually classified as command normals. It is important to be aware of this distinction, as some moves may be cancelable into special moves but not command normals.
Strategy Corner
It is possible to 
from a normal to a command normal during the active frames after hitstop has ended. This trick lets you retain the standalone properties of a command normal such as an overhead. This can let you pull out some overheads when an enemy isn't expecting them!