You signal that you are a reasonable person who does not let emotional attachment to a position cloud his judgment. If you're dealing with someone of higher status, you show that your mistake doesn't matter that much because you corrected yourself quickly. If you are dealing with someone who is lower status than you, you come off appearing magnanimous.

In many cases this is true, but someone could also interpret this as you as being loose with your morals, one who betrays one's own ideals in a flash (and so are untrustworthy). Or maybe interpret it as you being a follower, who only thinks what people tell you to.