(1) For years many astronomers have been saying that Pluto is not really a planet, but other astronomers and the general public have been insisting that it is. Now the IAU committee has fired back with essentially “OK, you want Pluto to be a planet? Fine. If you’re going to be that way, not only Pluto but Charon is also a planet now. You happy?” I doubt anyone on the committee actually thinks in these terms, but nevertheless that is the result.
(2) The Dawn mission has been planning to explore two asteroids (Ceres and Vesta) since the mission was first planned (and canceled and reinstated, etc.). If this new definition passes, the Dawn mission is all of a sudden now a mission to explore an asteroid and a planet (Ceres)! When it starts getting good pictures of Vesta, it may become a mission to two planets.
(3) The New Horizons mission has been on its way to explore the planet Pluto and other objects in the outer solar system. Now several months after its launch, it’s suddenly on its way to two planets.