Myside bias is very similar to confirmation bias (a subtype of cognitive bias), and some people use the terms interchangeably. In its specific meaning, it refers to our tendency to process information in ways that emphasize our existing beliefs. It is particularly prevalent in politics, but can also be seen in sports.
For example, a possible infraction in a soccer game will be seen as an obvious foul by one group of fans, but not by the other group of fans.