.exr is the prime file format for saving and loading floating point bit depths, and due to the library made to load and save these images being fully open source, the main interchange format as well.
Floating point bit-depths are used by the computer graphics industry to record scene referred values, which can be made via a camera or a computer renderer. Scene referred values means that the file can have values whiter than white, which in turn means that such a file can record lighting conditions, such as sunsets very accurately. These EXR files can then be used inside a renderer to create realistic lighting.
Krita can load and save EXR for the purpose of paint-over (yes, Krita can paint with scene referred values) and interchange with applications like Blender, Mari, Nuke and Natron.