Often, I think people say "that's biased" when they really mean "this isn't expressing my viewpoint". And here's one useful test: if you can look at something and decide that it's biased in 30 seconds, you haven't taken the time to examine the facts it presents and compare it to other presentations of the same facts. Of course, you can often read an article quickly and determine that no verifiable facts are presented, that it uses blatant propaganda techniques, etc., but when the article presents facts, dismissing them that quickly usually points to your own bias.Bias is an inclination or outlook to present or hold a partial perspective, often accompanied by a refusal to consider the possible merits of alternative points of view.
The people most likely to shout "that's biased" are often the least likely to be open to a careful, patient examination of the facts, especially if they might interfere with your existing point of view. And that's the textbook definition of bias.
But here's another problem: I think I can see your bias. You think you can see mine. We're probably both right. If we don't take the time for a patient, friendly discussion, neither of will learn.