Here's an example to illustrate.
Suppose you were promoting email marketing software for photographers. This is a discreet concept that can be expressed many ways:
email marketing for photographers email marketing for photographer email marketing photographer
The single concept, email marketing for photographers would get it's own 'ad group'. Other related concepts such as email list building for photography business are unique enough to merit a seperate ad group.
The reason why Adwords is organized this way is to ensure that advertisers are laser-targeted with relevancy.
It's in both your and Google's best interests to ensure that your Adwords account is generating as many clicks as possible, and by having separate ad groups you can custom tailor the ads within each ad group to be super relevant.
You end up with an army of 'mini sales people' that work 24/7/365. And that's Adwords alone. When you combine Adwords with SEO and email marketing to drive conversions you get a very powerful system indeed.