Usually translated as "short sword," kodachi is a Japanese word that literally means "small tachi." A tachi was a style of curved sword used in Japan from about AD 800-1400. As opposed to the katana used in later years, which was stuck in one's belt, edge-side upward, the tachi was slung from a sling edge-side down, and was generally slightly longer.
The more modern form of a short sword is known as wakizashi, which literally means "companion," and served as a backup sword worn edge upward as part of a matching pair with the katana. Although the terms are often used interchangeably, a kodachi technically differs from a wakizashi in that it is an older style of sword that would always be worn or displayed edge-side down.