The Krypt is a separate mode where you can spend Koins to unlock new Fatalities, Brutalities, costumes, concept art, and many more. It that can be explored in first person mode; however, you'll move from grid to grid, hence, the coordinates. It's quite hard to farm Koins especially if you're playing offline so you should prioritize unlocking the new Fatalities, then Brutalities, then costumes if you will. Unlocking all items in the Krypt will require hundreds and thousands of Koins.
The Krypt has different, separate areas. These areas are locked and will require Key Items which were equipment of some of the game's characters that are scattered in the field. Also, unlocking new areas give you additional Koins. Some chests also contain Koin stashes (though you need to spend a small amount of Koin to unlock them). There are also vanishing chests that appear and disappear in a fixed interval. These chests usually contain special items that can be purchased in a much cheaper price.
In addition, there are QTE's (Quick-time-Events) that will randomly trigger while you're exploring. These are usually deadly creatures that will ambush you, and you have to press the displayed button to protect yourself. The quicker you press the button, the more Koins you receive (Usually around 500 Koins tops). Failing the QTE won't have any negative impact in your exploration except the lack of additional Koins.