Training mode (or “practice mode”) is a mode included with nearly all home versions of fighting games. It is not often seen in the arcades, but Soul Calibur II, Arcana Heart FULL!, and Akatsuki Blitzkampf Auf Asche are among the few that do.
The primary usefulness of a training mode is that it is an easy environment to practice operating a character as well as their combos.
In the most basic circumstances, the opponent is a highly dumbed-down A.I. (the “dummy”) that doesn’t do anything but the most elementary actions (such as getting up after knockdown). Their life automatically recovers so that you do not perform knockouts.
Depending on the game itself, you may be able to set the A.I. to do slightly more advanced things, like standing, crouching, walking, blocking, jumping, and so forth. You might also be able to record an action for it, and most training modes these days allow another player to pick up their controls and operate the other character (in which cases, both characters act as the dummy, in a sense).
You may even be allowed to set the behavior of the power meter and other intricacies like counter hit effects, allowing extra convenience to test all manner of phenomena.