I will now list a few benefits that my clan has(which I'm an officer of).
*Weekly tournament cash prizes(fueled soley through donations)
*The ability to get into a chat channel of like-minded people and have a good discussion(very hard to do nowadays elsewhere )
*Have our own forum(http://ig.clan-infinity.net/smf/index.php?action=forum)
*A place where casters have numerous tournaments to train and try out casting.
*Competitive clan wars with other teams.
*The ability to spark an idea and put it into action with other people.
*And my favorite one, random people may actually know you when you go to an mlg wearing your clans tshirt(this actually happened :D)
How my clan progressed:
We started out on the very first day that chat channels were introduced. And that night, the eight of us were doing 4v4's against each other. This may sound meaningless, but it was some of the most fun I've had in Starcraft 2. We eventually started running clan wars and weekly tournaments, and we were growing at a stunning rate(around 10 new people a day). All the while we were training with one another for the various lans and leagues we were doing. And now modern day, a 5 month old gaming organization is now getting a live casted show match for 100$ against an extremely respectable and scary team, vVv.(Info here http://infgaming.net/smf/index.php?topic=1089.0)
And now here we are, my experience in a clan as an officer has increased my happiness with the game infinitely. There's always practice partners for me to train with, always events going on, always people on teamspeak to socialize with. And frankly, my personal goal for this post was to get more people involved with organized gaming, because there is oh so many who are missing out on all the benefits.
I highly recommend to anyone not in a clan to get involved with one! But how you say? It's quite simple, I generally don't recommend going to this website for the forums, but this is one exception.
http://us.battle.net/sc2/en/forum/13436/ (The multiplayer and esports section of the official forums)