According to Fred, his father gave him the family mansion while he and Fred's mother were away on a vacation to the isles. In the post-credits, Fred discovers a secret lair behind a painting of his family. Fred's father then appears to his son's amazement and reveals how he has once lived a double life as a superhero. Out of joy and relief of reuniting with him, Fred hugs his father, who hugs him back and tells him that they have a lot to talk about to each other.
Since the release of 20th Century Fox's X-Men in 2000, Lee has traditionally made cameo appearances in films based on Marvel Comics properties. Big Hero 6 marks his 22nd appearance in a Marvel-based film. As of March 2016, he has appeared in 24 films based on Marvel Comics.
Him being a superhero is a reference to his past role as the Mayor of Super Hero City in The Super Hero Squad, where he fancied himself a superhero. It could also be a reference to his role as the voice of the future version of Tony Stark in Avengers Assemble.
While his name is unknown, it is known that Fred's (and thus his) last initial is L, making it at least possible that the character's name actually is Stan Lee.