Original: Homer's middle initial "J", which stands for "Jay", is a "tribute" to animated characters such as Bullwinkle J. Moose and Rocket J. Squirrel from The Rocky and Bullwinkle Show who got their middle initial from Jay Ward.
Simplified: Homer's middle initial "J," which was discovered to stand for "Jay", was a "tribute" to Bullwinkle J. Moose from Rocky and Bullwinkle, a show Matt Groening loved as a child.