Showrunner Dave Filoni discussed this in an interview with IGN. The very short answer is that the show was intended to be fun and accessible for all of Star Wars' fans, including those small number of fans (no, seriously. They do exist) who actually quite like Jar Jar.
But I think in the end, with 100 episodes of Clone Wars, no matter
what type of Star Wars fan you are -- and I think that’s something a
lot of people miss; there are a lot of types of Star Wars fans, and by
now they want different things out of the saga. Some people want it to
be like A New Hope, some people want it to be very dark. Some people
want it to not be about main characters and about side characters. You
know, everybody has a different need. Clone Wars, by the nature of the
way George had to tell the stories, covers a lot of that. So if you
just like bounty hunters, we’ve got that. If you just like Sith Lords
fighting Sith Lords, we’ve got that. Sith Lords fighting Jedi, we’ve
got that. Force gods that you never thought of, we’ve got that. Just
about R2-D2 and C-3PO, got that. If you are a holdout Jar Jar Binks
lover, we’ve got that. A whole range of clone people, we’ve got that.
There was something to satisfy everybody in the end.
Additionally, in the Bombad Jedi featurette on Starwars.com, Filoni explicitly states that George Lucas personally insisted on Jar Jar's inclusion.
Filoni: Early on, George expressed an interest that because we're in this time
period, the Clone Wars, that he wanted to see Jar Jar again and Henry Gilroy and I felt that perhaps an animated venue, like The Clone Wars is gonna fit really well for our friend, Jar Jar.