Breakfast in the park (this is what its called now) is only available to you if you are a guest of the Santa Fe, Cheyenne, Seqouia Lodge, or Newport Bay Club hotels.
You can't book it in advance, you have to ask at your hotel reception for it. Its not on every day, and its subject to availability and numbers. Its one restaurant in the main park which is open for this breakfast, Disney chooses which one, out of typically the Plaza Gardens, Chalet au Marionette, or Pizzeria Bella Notte.
Its the same standard of breakfast as the Sequoia Lodge and Newport Bay Club (so a slight upgrade on the Santa Fe or Cheyenne breakfasts). No characters, and its instead of breakfast at your hotel.
You get timeslots for this, they run from around 8.15am I think, until around 9.45am.
I love breakfast in the park, if we're at the Santa Fe or the Cheyenne I try to get this for every morning of our stay if its available, and we try to get a 9.15 or 9.30am slot. That way we can do the first and much quieter hour of EMH from 8am, then have breakfast without leaving the park at all, and then be ready for ropedrop or the start of the Studios day.