What is Karaite Judaism?

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Google my friend. Use it.

A fast attack militant sect within the Jewish community. As the other poster suggested you should look it up.

Karaite Judaism is that branch of Judaism which believes that only the TaNaKh contains the divine revelation from God. Karaite Judaism is based upon three foundational elements: 1. That the TaNaKh (the Hebrew Holy Scriptures) is the divine revelation of God; 2. That logical or reasonable interpretation can be used to determine the intent of the law; and 3. Inherited Tradition which they call Sevel Hayerusha. Karaite Judaism's "Golden Age" started with Danyiel al-Kumisi, who according to the Jewish Encyclopedia was "one of the most prominent Karaite scholars of the earlier period; flourished at the end of the ninth or at the beginning of the tenth century;" The main difference between orthodox Judaism and Karaite Judaism is over the issue of the existence of an 'oral Torah' which Orthodox Jews believe was given to Moses.

They don't accept the Rabinic precepts, they follow the Tanakh alone.