You may have heard of the game "Chinese Whispers" or "Broken Telephone": someone thinks up a sentence and whispers it to the first person. That person whispers it on to the next, and so on, until it arrives back at the first person. Invariable, the message will have changed in minor or major ways because someone mis-heard, which is what makes this amusing.
The Conlang Translation Relay is similar, only with conlangs: the relay "owner" comes up with a short story and translates it into his conlang of choice (if it's not an original story), then sends it to the first participant along with a glossary and a short sketch of the grammar or whatever else is needed to understand it. That participant understands the story, translates it into English and into his own conlang.
He then sends both English and conlang versions to the list owner, and only the conlang version (again, along with glossary, notes, etc.) to the next participant. At the end, all the versions are sometimes put up on a web page along with the English translations and you can see how the text has "evolved" :).
One of the interesting parts here is that you get not only misunderstandings but cultural clashes—for example, a conculture may not have an exact equivalent of a certain word so the participant uses a conlang word which means something different, or a conlang may lack a concept and the creator doesn't wish to come up with a word for it in his conlang so he re-phrases somehow.
If you're interested, join the "relay" mailing list! Then, if you want to participate with a conlang of your own, either e-mail the list or the this relay's owner directly, Amanda Babcock (at email@example.com or firstname.lastname@example.org).