What does this "Challenger" icon mean?
Solution 1:
That's an unused indicator of your MMR rank for an upcoming patch that will add a Competitive mode.
In Closed Beta, there was competitive matchmaking and as such that image you posted is the default image displayed on the Competitive Play screen.
Note that currently Overwatch does not have a competitive matchmaking system; this answer will be updated appropriately when it is added.
You can see the same format in this gif Blizzard provided showcasing what competitive ranking will look like.