What are the files in /dev/input/ and what they do?

This is the location where device files for your input devices are located.

Device Files: (taken from Wikipedia)

In Unix-like operating systems, a device file or special file is an interface for a device driver that appears in a file system as if it were an ordinary file...They allow software to interact with a device driver using standard input/output system calls, which simplifies many tasks and unifies user-space I/O mechanisms.

/dev is system directory that contains all Hardware device related files. Check out this manual for Ubuntu Filesystem Tree Overview and this also.

All the information in /dev/input/eventX is stored in a structure called input_event. More details about the event are available here: https://www.kernel.org/doc/Documentation/input/input.txt