They are the rights granted to a person that allow said person to boast on themselves to a certain extent without being looked down on for it.

Bragging rights may be granted to a person for (but not limited to) the following reasons:

-An Amazing Achievement
-Attaining something greatly desired by many people
-An unfortunate event that can be viewed as positive for different reasons

However, using bragging rights after their expiration date may lead to extreme dislike of said person.
Example 1:
Scholar: Finally! After so many years I finally attained my Ph.d in Quantum Physics
Average Person: Congratulations

Example 2:
Contest Winner: WOOT!!! I called in to a radio station and scored 2 tickets to see Rammstein in Berlin with free air fare and hotel. Plus, I get to have lunch with Till Lindemann !!!
Average Person: Congratulations

Example 3 (Misuse of bragging rights):
50 Cent : Yeah, I'm gangsta. I got shot 9 times. Even in the face. My music sells, I'm rich, and women love me.
Average Person: No, you are not gangster. Anyone can get shot in the arms, legs, and jaw and survive it. Your music sells because you have Eminem and Dr. Dre behind you. Furthermore, women do not love you, they love your money that you don't deserve.
by Zen Master Alvey August 24, 2007
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The informal right to brag and boast about an achievement you've made. You get this right after you've achieved it.

If you make it up, you might get away for a while, but you'll get bashed if they find out you never earnt this right.
Geek A: *Three headshots in Counter-strike in 30 seconds*
Geek B: Bastard, you shot your own team mates
Geek A: But it was still 3 headshots, that means I get bragging rights
Geek B: You're a load of shit, no bragging rights for stupid noobs.
by Skyboy September 5, 2005
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the privilege of boasting about one's achievments
needless to say getting through there would get him bragging rights for several weeks.
by The Return of Light Joker September 3, 2009
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