A brand new theater, designed much like the current one and expected the hold the same number of guests, will be built in the Western side of the Africa section, off a path leading from the Tusker House restaurant. There are no major plans to change any of the show's content when it opens in its new home. The park also isn't quite ready to say when the performance will move, or if there will be a period where the show is dark during the transition.
The current theater for the Festival of the Lion King is in Animal Kingdom's Camp Mickey-Minnie, which is said to be the future home of the Avatar land. Really the entire land as it is contains a bunch of meet and greet areas, and the Festival theater. Fans of the park have grown to love the show enough that they chose to build it a new home instead of retire it.
There has been some speculation that the Avatar project isn't moving forward with the steam that many thought it would have, and fans have had some seriously mixed reactions to the plan. However, it seems like it could still be in the works since they're spending the cash to move the Festival show. An interesting development, it will be even more interesting to hear more news of what Avatar may hold and see if the bulldozers start to roll in.