Pokédex: Allows you to look at the pokémon you have caught and seen. Faded images are pokémon you have seen but not yet caught. Blank squares are the pokémon you have neither caught nor seen. It also gives you info on the pokemon you have found.
Mapdex: Allows you to search for a pokémon, area, or item. Keep in mind that any event pokémon or legendary pokemons will not show up in the results. Alternatively you could click on one of the links to the five regions right above the searchbox.