Nothing really, it's just something to show off on your profile. But seeing only other people can give it to you, and just once, it's thought of as a token of love and/or respect.
Oh and if you were slightly confused about what I said, I'm kind of a fan of poker games. Too bad though I haven't been able to play them recently.
They're easy to give, just click on someone's profile (mine for example), under the "Give" tab in the top-right search for "Give a Llama Badge", then type in your password and pass on the llama. Easy-peasy.
Hope that makes sense. In the meantime, take care.