The Experience Chart shows you the required experience for each level and the total experience you would have accumulated. It only goes up to level 55 because that would already be an insane amount of time. I can't quite figure out the equation used to produce it.
The Specialties Chart shows you the five different specialties in the game. Each Specialty has its own tab that shows you the increase/decrease damage, the Digimon that are that specialty (with a link to the Digipedia), and the Skills that are that specialty (with a link to the Skills page).
The Type Chart shows you the three different Types. Each Type has its own tab which shows all the Digimon of that specific type (with a link to the Digipedia).