"Hatzi" means "half". This prayer is called "Hatzi Kaddish" because it is a short version of the Kaddish.
There are several versions of the Kaddish. The word "Kaddish" comes from "Kadosh", which means "holy" or "sacred" or "set apart".
This is a prayer of praise written not in Hebrew but in Aramaic.
This particular Kaddish is used as a transition between different parts of the service.
We sing different melodies for each different service. The melody I sing it is the one we use for before the Maftir on Shabbat Morning & before the Amidah for Maariv L’Shabbat.
