My Brain is Full of Fuck is a catchphrase that is often used in response images, which shows a character with his/her hands wrapped around head, as if struggling with a severe migraine. The images are mostly used in response to a post or thread that is deemed unworthy or pointless, signifying that one's brain has been severely affected by the stupidity he or she has been exposed to. Also see: Facepalm.
One of the earliest image macros featuring the tagline can be found on a MyConfinedSpace blog post uploaded by user TikiGod on February 27th, 2008. The image depicts one of the Gargoyle sculpture ornaments found on the facade of Magdelen College building at Oxford University, United Kingdom:
The most widespread instance didn't break out until late 2009, when MemeDepot user DarkSky Forever paired the phrase with an image of Jackie Chan looking very confounded and posted it on the site on September 30th, 2009.
Aside from the original image, the phrase has been adopted into other pictures and spawned a handful of popular derivatives, such as this graphic illustration by Japanese manga artist Shintaro Kago (originally featured as cover art of Vice magazine, February 2008 issue):
Another semi-popular derivative is a series of pictures featuring late scientist Carl Sagan with a modified tagline "My Brain is Filled With Billions and Billions of Fuck", in reference to the line "A galaxy is composed of gas and dust and stars--billions upon billions of stars" from his Symphony of Science video "A Glorious Dawn":
Here's an example of this particular derivative: