Okay, so basically, Shining and Twilight have this little toy tinfoil crown for frequent competitions when they were little, including kite-flying and getting good grades, and whoever won the most competitions at the end of each week would earn the crown as well as the title of "Sibling Supreme". Twilight and Shining agree to have one final showdown and the winner is the Sibling Supreme for good. Back at the castle, Twilight goes on to enlist the help of their friends to get the crown.
I'm just going to make a long story short here. Spike ends up winning the crown with Luna's help, everyone just accepts it, and that's my biggest pet peeve of this episode. The only reason Spike won the whole thing is because of Princess Luna. That, in my opinion, is an unfair advantage.
Adding on to that, Spike isn't Twilight's brother. He's her pet and slave. Always has been. Always will be.