A kanai is a zealot, someone who advocates extreme action in response to conflict. The root is the word kinui, which means jealousy, envy or passion. (Hamekaneh ata li? Are you jealous on my account? Moses asks Joshua, after being told that others are prophesying in the camp).
The most famous kanai in the Torah was Pinchas, who slew a tribal chief and his Midianite partner. Gods response was to stop the plague that had been killing those who had been intimate with the Midianite women and worshipping idols. God credited Pinchass zealousness with having turned back His anger, by displaying among them his passion for Me (bekano et kinati), so that I did not have to wipe out the Israelite people in My passion (Numbers 25:11).
The Great Revolt that led to the destruction of the Second Temple was led by the Kanayim. They abided no compromise with the Romans and even destroyed stockpiles of food that would have seen the Jews of Jerusalem through a lengthy siege, ensuring that the Jews would have no choice but to fight the Romans (Talmud Gittin 56a). Theirzealotry failed and contributed to the suffering of the Jewish people.
Kanaut is obviously problematic and the talmudic analysis of Pinchass act reveals an ambivalent attitude. However, every generation needs its zealots to resist attempts to deny the Jewish people their right to independence and self-defence.