Bias refers to language that supports an ideological position, either explicitly or implicitly. When we see subjectivity in pieces of writing that should be objective, we can claim that they are biased. When we see an imbalance between opposite perspectives in an article, then there is evidence of bias.
For example, an article in the New York Times once explored single motherhood, using the following phrase: "It used to be called illegitimacy. Now it is the new normal." This is very suggestive. The language insinuates that the term illegitimacy should still be applied to single motherhood.