Have you ever had the moment where something comical happens, and you never expected it to? And the people that saw it happen laugh whenever it's brought up, but anyone who wasn't looks at them and wonders what could possibly be so funny?
It's an inside joke, they say.
But that's just it. Inside jokes don't even have to be a joke or even funny. Sure they can make you smile, but it's usually from the memory of what happened or the knowledge of what it really means. This happens all the time with friends in reality, but a really unappreciated form of the inside joke is in writing.
It isn't always meant to be funny. Sometimes it's just meant to be a nod to a great achievement or a fandom that had no idea the author was part of it. Sometimes they make you feel smart when you catch them, and some make you chuckle whenever it's brought up because you recognize the source. And the glory of it all? It's hidden away underneath the story for only the observant and knowledgable to catch unless the author wants people to know about it.
To throw two examples out from the top of my head:
In Paul Crilley's novel The Lazarus Machine, there is a computer genius character who goes by the name "Stepp Reckoner." Every time she is introduced, everyone asks about her name and it is re-explained this is not her real name. I must give a shout-out to Mr. Crilley for this one, because it almost passed me by. For those who wish to know, the first calculator capable of performing all four arithmetic functions was invented by Gottfried Wilhelm Leibniz and called the "Stepped Reckoner."
Another that comes to mind is Christopher Paolini's Brisingr, in which two of the main characters talk about "the lonely god." In the author's note at the end of the novel, he commends those who caught the reference and comments that the Doctor can travel anywhere, even alternate realities. Later, there is a reference to a comical planet name from Doctor Who wherein Angela the herbalist says, "Raxacori- Oh never mind. It wouldn't mean anything to you anyway."
There are tons more in any genre you might be reading. Watch for them. They're authors' way of saying 'Hey! I'm a normal person just like you!' even if it's from behind the words of a story. They want you to recognize them, else they wouldn't put them there.