There are eight mini challenges. Each challenge is located in it's own folder under firmware. You don't have to complete them in order, but I would recommend starting at challenge1.
In each challenge you need to find a flag. The flag is made up of two bytes to create a 16-bit number. For example 0x0001 in hexidecimal is the number 1, and 0xFFFF is the number 65535. See here for more info on hexidecimal number representation.
Once you have a flag, you can update them in the firmware/solve sketch, and program your badge. This sets all your EEPROM values to the flags you have collected.
To see your progress, you can program back your original badge firmware/badge.
Once you have successfully found all challenges, find @jsstott to verify your solution.