The dispute finds its roots in a character called Jim Brockmire, who appeared in a Funny Or Die skit in 2010. (A character Azaria claims he created as far back as 1983 whilst at college.)
The sketch is said to have led to various possible movie opportunities for Azaria. However, actor Craig Bierko is also claiming he had a part in creating the voice of Jim Brockmire. "(Bierko's claim of ownership) has created a cloud over the rightful ownership of the Azaria Voice (which is an integral part of the Jim Brockmire Character) such that Plaintiffs' ability to develop a feature length motion picture based upon the Jim Brockmire Character is being significantly impeded," reads the Lawsuit. The Simpsons actor is seeking a declaration that Brockmire is a copyrightable character. He also wants the court to declare that Bierko has no claim to the character, but is seeking no monetary compensation apart from legal fees.
Azaria is a major player on The Simpsons, being the voice behind Comic Book Guy as well as the aforementioned Chief Wiggum and Moe Szyslak. He's been part of the team since 1989, but current Simpsons fan shouldn't worry, as their favourite characters won't be affected.