A committed partner in a long-term bromance.
Dirk: Hey, you wanna go to the bar tonight?
Lewis: Maybe but I'll have to check with my significant brother first.
What two bros in a bromance call eachother. Not to be confused with a homosexual relationship, using this term signifies a strong friendship between two completely straight males. Significant brothers have love for eachother but are not in love with eachother.
Girl: Are you gay?
Bro: Nah, I just have a significant brother.
Some Kid: Do you know Sean?
Some Bro: Know him? Bro, He's my significant brother!