No one really knows for sure why IBM is called Big Blue, but the earliest-known reference to the nickname comes from an IBM loyalist in the early 1980s. In a "BusinessWeek" magazine article, in the June 8, 1981 issue, the diehard fan said, "I don't want to be saying I should have stuck with the 'Big Blue," and then added, "The nickname comes from the pervasiveness of IBM's blue computers."
The misconception is that the reference came from employees and is used by employees. That's definitely not the case. However, the word "blue" is in the names of IBM supercomputers, such as Deep Blue and Blue Gene.