Continued,
The sad part is that most people have the wrong idea about them because they've never been taught exactly what they are or what's inside.
Part of that is the fact that most martial arts were introduced to this country by servicemen returning from Okinawa and Korea. In Europe we have a saying, someone who speaks 3 languages is tri-lingual, someone who speaks two languages is bi-lingual and someone who speaks one language is American
So, even if the Oriental instructors had taught by explanation there was a language barrier. To make matters worse any one who's trained under a Japanese or Okinawan instructor knows they don't teach by explanation buy by demostration. Their belief is that the voyage of self discovery is the proper way to learn. Unfortunately, those same military guys who came back here to teach ran into a bunch of students who, unlike their oriental counterparts, wanted to know why they were required to do certain things. Rather than say, "I don't know" they often just made stuff up, or taught the very obvious.
As a result forms became little more than dances that one had to learn to pass their next belt level. I've taught at karate college, started breaking forms down, and ended up with the entire college in my class. The people who were supposed to rotate to the next class with Bill Wallace and Joe Lewis didn't go....not because they don't think those guys are any good (they're brilliant at what they do) but because they hadn't ever seen the katas taught properly and were fed up with sports applications. (Most school owners forget that the main reason people join martial arts schools is for self defense).
I've also always been big into multiple opponents. At my size I don't get attacked one on one much

and I've always believed that is the martial arts forte. Whereas boxers for example train to go ten rounds with one man, I train to go one round with ten!! Katas are one of the only training exercises we have to fight multiple opponents. Sparring doesn't do it (unless you spar multiple opponents), bag work doesn't do it, ground fighting doesn't do it. Only katas (and sparring multiple opponents) do it.
The reason the forms are prearranged is, as Misshinryu said, to teach you different skills. The first kata in my Combat Karate is Nai Han Sin. It's a form designed to teach you to fight multiple opponents with your back to the wall. Sanchin teaches you breath control and how to fight when winded, San Sayru teaches using body weight etc. The idea is that by the time you get through the system you've learned all these different aspects of fighting which makes you a very versatile fighter.
Once we taught someone the form then we'd go back inside and practise the individual moves against multiple adversaries, not unlike the combat scenarios that Hock teaches.
Hope that explains them a little better to some of you who may have been short changed going through your training.
PS: This isn't a dig at instructors who didn't teach them properly. Most of them are only passing on what they've learned, and, if they weren't taught properly to begin with...well, you can see where the problem lies.