When one thinks of a cartoon director, the chances are names like Chuck Jones or Tex Avery comes up. The jobs these directors did varied by the studios and the directors' preference, but for the most part they acted out animation, decided on how the story should go, how the characters are designed, how the character's voice should sound, how it should be timed, and a ton of other stuff.
This was in the days of Looney Tunes, which was more than 50 years ago.
In modern sense, especially in television, the job of directing a cartoon really varies, depending on the studio, the show, and how it's set up.
In some cartoons, a person listed director basically fills out the timing sheet for the overseas animators to follow. They rarely have input in the story structure, the designs, or directing the voice actors (usually the show's creator does all or part of that).
In script-driven cartoons, the director is involved in visualizing the scripts for the storyboard artists, although the level of power varies greatly depending on the show. In those shows they rarely do the timing, often giving out sections of storyboards for other timers to fill out.
It's no secret that each section is separated by levels. Many animation fans scoff at this, saying it's too segmented, but I don't think it's an awful system. As long as there is at least one creative head who is de-facto in charge of all the departments (whether it's the creator or the show-runner) there should at least be some consistance. Knowing the strict deadlines in TV animation, it's not too bad, and as long as you have the right people it's still capable of producing good cartoons.
That said, I'm curious to know what others view about this.