Geocaching provides a very large social network with geocachers connected by finding each others caches. To keep it simple let's just consider multi-caches.
A cycle is a sequence of caches that connect cachers ultimately leading back to the original one. For example, consider the following sequence of five multi-caches:
GC2WF9G(Sea Lions Redux) by seldon who found
GC2RD1F(The Amazing Technicolor Dreamcache Too) by bflentge who found
GC2MDKE(Quit Your Horsing Around) by Boreal Walker who found
GC2WA8N(Choose Wisely) by JustJackMN who found
GC1R78K(Hugs & Kisses) by Smokey&Blondie who found
GC2WF9G(Sea Lions Redux), completing the cycle.
This is called a 5-cycle because it's a cycle of 5 caches. You are to find a cycle of at least 9 multi-caches that form a cycle.
In your log, list the caches in your cycle, including the caches and cachers in order, as in the example above. Of course, in addition to finding and logging the nine multi-caches in your 9-cycle you will need to find and log the cache at the posted coordinates.