First thing the understand is that isn't really a quote by "Stephen Colbert" the person it is a joke made via "Stephen Colbert" the character from the Colbert Report which was a caricature poking fun at Bill O'Reilly (mostly).

This character is a conservative infotainment host. And so when reality ultimately flies in the face of his conservative viewpoints the joke is that he merely dismisses reality because "reality has a liberal bias".

Within this context I imagine the argument is that in many cases what is perceived as a "political bias" by some might just be considered "reality" by others. For example there was the issue from the early 2000s of "teach the controversy" where some conservatives would have argued answering truthfully about the scientific consensus on evolution or global warming was "leftwing bias".

The most important thing I think is that it is a joke that simply rings true with a lot of people as time has passed.