If you've ever tried building a slightly large application, or one at all complex, things can quickly get out of control. I don't know how many projects I bailed on when I was first starting out because I didn't know patterns, or how to make parts of the system communicate without being tied to each other, or dependent on each other.
So, basically a framework is a collection of patterns put together. Theoretically, if you learn to follow the "rules" of a (tried and true) framework, your app will not get out of control to the point where you find yourself fixing one bug and causing two. I've been there and it's not fun.
I also found that by learning to use a framework you initially don't have to know so much about the patterns behind what you're doing. But before long you'll get a good handle on the patterns used and you'll be able to apply them in new situations or find a better pattern. So it's a good learning tool as well.
I'm sure people will have arguments against using frameworks -- this is just my experience. But if you become familiar with a few, you will likely find that one might be suitable for one project but not another.
As far as Flex frameworks, I personally like PureMVC. In all honesty the only other one I've given a good amount of time to is Cairngorm. But I like PureMVC because it feels right to me, but also it's generally not dependent on so much on the built-in Actionscript classes. For example, it uses it's own notification system. So if the notifications change in Flex, they'll still work in your PureMVC app. Also, the creator Cliff is super helpful in his forums, and he's really passionate about it. And the documentation is great.
I recommend coming up with a super basic app, and building it without any frameworks, then again with a couple others. You don't have to finish the app, but just get a feel for what's behind the frameworks.