Bragging Rights keeps track of all the mobs that you (and your raid/party) kill, assigning a point value to each based on the mob's level, your level and the mob's classification (normal, elite, rate etc.)
Brag is configured via Blizzard's Interface options (or you can use /brag to open the window directly).
Brag has several configuration options:
Enable Debug Output: Shows various messages concerning the inner workings of Bragging Rights. Be aware that this will likely be very spammy as every kill and every time someone in your raid changes targets you will get a message. This option should be normally be left off.
Reporting Format: This dropdown has two options: Text and BBCode. It controls the format that the big report is displayed in. BBCode format includes links to the armory and WoWHead.
You currently have x points! Shows you how many points you've earned so far. The report button will output this to your Guild Channel.
Reset Scores: Resets the number of points you have earned (does not erase the list of killed mobs).