A chapter is a campus branch. That's oversimplifying it a little as there are alumni/graduate chapters and others too, but it's an easy way to understand the concept.
Media portrayals (films and the like) have to be sell-able. Consequently they will focus on things like partying, attempt to portray greek orgs as having wild nights (preferably with beautiful, tanned and athletic people); after all, these aren't generally documentaries so the portrayals - due to editing or scripting - may be very inaccurate. Additionally, some chapters of some groups might focus more on socials/parties than a varied blend of social activities, academics, philanthropy, leadership etc. Social activities are important and fun but there's a
lot more to greek orgs than them. Like someone said "you don't have to choose between fun and success, the most successful people seek both".
You can try to get into more than one, although you can only be a member of one group, generally. Many NPC (governing body of 26 womens' sororities) groups hold formal 'rush' (recruitment) and this gives the girls at a college campus a chance to visit all the houses and chapters, the person rushing might have 2 sororities which are their top choices. Eventually the process of mutual selection has them find their group.
Broadly speaking, the "greek" aspect is simply because they are named with greek letters. MysticCat81 does a great job of filling in the gaps, above. Dekeguy,
elsewhere on this message board explains it excellently too.
Rituals, like someone else said, are present in everday life; teethbrushing, graduation etc. Obvioulsy greek rituals might mean more than brushing teeth
. The concept of secrecy is generally based on a premise that you get out as much as you put in. Taking part in fraternity activities (
NOT hazing), learning about the group etc, versus just being able to see the ritual on a website/book allows it to be worked towards. And, thusly mean more; which means one is likely to embody the groups ideals more since it is something they have worked to be a part of. Whether those ideals be integrity or whatever. It also gives a connection with the past, with all brothers and sisters who came before you. Something shared that sets you out. If this interests you further, you might take a look at
www.tke.org, Tau Kappa Epsilon fraternity. They have a document called 'why secrecy in rituals' on their website.
As for hazing... to answer your questions directly: Historically hazing was used (and it was not used everywhere) on the basis it weeds out those who aren't really committed and means that those who are prepared to spend long nights etc must really want to become brothers/sisters of that group who'll have a strong bond. Today, hazing is banned by every national greek umbrella organisation and greek org. Chapters would risk having their charter (permission to be a chapter) revoked and the members of that group expulsion from that fraternity. To say nothing of criminal charges or discipline from the university. It is abomination of the ideals of such groups. There may be isolated pockets of the activities... but they are not responsible members of greek life. All it "proves" if "endured", is that you've "earnt" [note sarcastic quote marks!] your place in a group which should be reported and which threatens greek life everywhere.