Judges are vital parts of a family's connections, they are needed to get family members out of jail sentences, or to give lenient sentences.
In New York, Vito Corleone owned most of the Judges in the city, which irritated the other Dons, who wished to share their influence to help with their involvement in the narcotics trade. After the summit following Sonny Corleone's demise, Don Vito agreed.