I take Left Hegelianism to be a philosophical tradition/position that takes Hegel’s philosophy, and radically orientates it to be anti-capitalist and anti-authoritarian.

An example of Left Hegelian literature or philosophical figures would be Marx, Proudhon, and, say, Ludwig Feuerbach.

Wikipedia has quite a good paragraph that sums up the more-or-less agreed position that all the Left Hegelians had:

The Young Hegelians drew on both Hegel’s veneration of Reason and Freedom (as the guiding forces of history) and his idea that the 'Spirit’ overcame all that opposed reason and freedom. They felt Hegel’s apparent belief in the end of history conflicted with other aspects of his thought and that, contrary to his later thought, the dialectic was certainly not complete; this they felt was (painfully) obvious given the irrationality of religious beliefs and the empirical lack of freedoms—especially political and religious freedoms—in existing Prussian society.