The term "Tutsi" is actually an indeterminate term. In the Kinyarwanda language, a single Tutsi is termed batutsi, and more than one (the plural) is termed watutsi. This is the source of the dance name "Watusi".
The Watutsi are actually the most recent arrivals in Rwanda and Burundi. The original inhabitants were the Twa (or Watwa), a pygmy people. The Hutu (Wahutu), a Bantu-derived people, subsequently moved in and dominated the Twa. Later yet, the Tutsi immigrated and dominated both the Hutu and the Twa, establishing kingdoms that they ruled.
An interesting aspect of these three racial groups is comparative height. The Twa are traditionally short, the Hutu medium, and the Tutsi tall (traditionally; more modern interbreeding is reducing these differences).
The disparities between the rights of the racial groups were not as extreme as in many such cases, but they were significant. The Hutu were basically considered to be the laborers for the Tutsi. If a Tutsi murdered a Hutu, the Hutu's kin could kill the Tutsi in revenge, but if a Hutu murdered a Tutsi, then the Tutsi's kin could kill the Hutu and one other member of his family in revenge.
In recent years, both Rwanda and Burundi have been, at least in theory, democratic nations with the same rights accorded to all. Nonetheless, the Tutsi have still held most power, with great resentment building on the part of the Hutu, leading to the recent massacres.