Used to describe two things that are independent of each other. One does not imply the other.
Common sense and intelligence are orthogonal. I've seen plenty of smart people with no common sense.
A word used by the tech-savvy to sound smarter than the really are.
A math term that means perpendicular, but not just in 2D but in any dimension. Now commonly used to indicate an idea or concept that stands apart so much from everything else that it "sticks out," is "from left field," or is "third-way."
"I have this co-worker who keeps using the word 'orthogonal,' usually after he mentions some idea he thinks is God's gift to man. Can't wait to get this word into my vocab. Soon as I figure out what it means."