A meme is something that spreads rapidly, becoming well known, usually around the Internet. The Simpsons has spawned a couple of memes over the years. An idiom is something that originated from something like a TV show, book, movie etc. but has became commonly used.
"That's a paddlin'"
Dead Bart is a story on Creepypasta that has become well known over the Internet. Many fans have been led to believe that it is real, although it is not.
The goggles do nothing!
Originating from the quote by Rainier Wolfcastle "My eyes! The goggles do nothing!" from the episode "Radioactive Man", the quote has been shortened to simply "the goggles do nothing". It is now a popular catchphrase used for conveying the horror of having seen something unwanted.
"Milhouse is Not a Meme"
The phrase "Milhouse is Not a Meme" a paradoxical statement and a well-known debate on 4chan about what makes an Internet meme and what doesn’t, using The Simpsons character Milhouse Van Houten as an example. Since the birth of the debate on 4chan in 2005, the phrase has been typically used to initiate a chain post of recursive nature. Due to its recurrence over time, “Milhouse is not a meme” is often referred to as a forced meme.
Cheese-eating surrender monkeys
"I, for one, welcome our new insect overlords"
While not originating from The Simpsons, meh has been thought to be popularized by the show.
D'oh has been added into the Oxford English Dictionary. It is commonly used by people both over the Internet and in real life.