In the clip linked above, at first Penny (Kaley Cuoco), Sheldon's neighbor and show guest, tries to help Sheldon improve his robotic presentation style. As usual, he completely misinterprets her perfectly reasonable suggestions, to comic effect. By the end of the scene, Sheldon finally gets to the topic of flags. He bluntly declares that Nebraska’s -- Nebraska being Penny's home state -- “is simply the state’s seal on a field of blue.” He offers no other information and then the scene ends.
The joke, of course, is that Sheldon is into arcane, nerdy things just for the sake of being into them. He’s a weirdo, but an ultimately loveable one. Because he is such a self-serious know-it-all, he makes for a classic sitcom character.
This is all good. I get the joke. At first glance it is pretty esoteric, taking such an active interest in the colorful rectangles of cloth that we put on poles.
But I don't mind. The stigma of geekiness aside, I still think flags are worth learning about and discussing. Looking into the details of the lore and designs of flags and seals as a “shorthand of history,” as vexillology has been called, is a perfectly fine lens with which to better understand the world.
So thanks, Sheldon, for bringing it up. And Happy Flag Day.
P.S. There basically is a real-life version of "Fun with Flags." It's called "Flag Friday" and is hosted by Paul "Barby" Barbato of the YouTube channel Geography Now! Check it out, it's a lot of fun.