The person who is basically your best friend. You tell them everything and they tell you everything, but people don't really know you are best friends or don't expect you to be best friends because you are very different from each other.
Person 1: Yeah, that's my best friend, you didn't know?
Person 2: REALLY?! That's so unexpected! He's so well-known! You're...yeah.
Person 1: Yeah, we're secret best friends. People don't really know about our friendship, but we've been best friends for a really long time.
Mahesh is my secret best friend.