Karaite Judaism holds that the commandments given to Moses are contained in the written Torah alone, and that the rabbinic Oral Torah (the Mishnah, the Talmud, and the whole structure of interpretation built upon them), has no binding authority.
The name comes from the Hebrew for readers, or scripturalists. The method is peshat, the plain sense of the text, arrived at by study, by reason and by the shared usage of the community, with each Karaite bearing the responsibility to read for themselves rather than deferring to a chain of authorities. The nearest thing to a Karaite motto is the instruction to search the scriptures well and not to rely on anyone else's opinion: including, explicitly, that of Karaite teachers.
The practical results diverge from Rabbanite Judaism at many points. The calendar is fixed by observation of the new moon and by the state of the barley crop rather than by calculation, so festivals can fall on different days. The Sabbath prohibitions differ. The dietary rules differ, since the prohibition on cooking a kid in its mother's milk is not extended into the rabbinic separation of meat and dairy. The laws of marriage and of ritual purity differ. Karaites prostrate fully in prayer, and the liturgy is drawn overwhelmingly from scripture.
Karaites also count the fifty days to Shavuot from the sabbath after Passover rather than from the festival day, which places that festival on a Sunday every year. The disagreement is very old: the Sadducees are recorded as having had it with the Pharisees centuries earlier.
It is not a modern protest movement. It is a Jewish tradition roughly as old as the Talmud is in its finished form.