An owner who goes against common beliefs, whether that be by making out of the ordinary draft picks or with seemingly strange starting lineups.
A contrarian goes against the grain, they take players that aren't as coveted in an attempt to make up ground on their opponents. Contrarians employ a high risk/high reward strategy. They buy low on players with potential upside and for the most part avoid players that are consistent.
On occasion a contrarian will also draft a superstar, but only when no one else is interested in them. This could mean they are facing a touch matchup or coming off injury. The primary purpose of being a contrarian is to select good players that aren't being taken by others.
They could either draft a team full of players that are unexpected or set their lineup in a way that is unexpected. Contrarians keep you guessing as to what their strategies are.
Being a contrarian isn't necessarily a good or bad thing, it sometimes pays off while others does it. By going outside the box and going against what is thought to be normal the contrarian allows themselves to make up or lose ground.
In daily fantasy challenges when playing against a lot of people, being a contrarian is actually a good thing. Many competitors will select the big name superstars, meaning that if that player does well, you do not gain anything on the masses. You have a better chance of drafting a lesser known player with high upside. For example, instead of selecting Julio Jones, take a Keenan Allen type player who might be flying under the radar. That way if they do well then not as many people will be reaping the benefits.
It is recommended to be a contrarian in leagues where you compete against high amounts of people, however in a standard fantasy football league it is better to pick sure things in the early rounds and then in the later rounds go for high upside players.