Why two communities for Mathematics? Wasn't one enough?
The two sites are meant for very different audiences, and have very different types of questions.
From the MathOverflow faq:
MathOverflow's primary goal is for users to ask and answer research level math questions, the sorts of questions you come across when you're writing or reading articles or graduate level books.
From the Area51 page for math.stackexchange:
Q&A site for people studying math at any level & professionals in related fields
Why separate the two? The community at MathOverflow is not interested in the typical question here. It is too elementary, and they don't want to be flooded with people asking basic math questions. Conversely, most MathOverflow questions would not be well suited to the audience here. Many may not even be comprehensible! The concentration of professional mathematicians is too low (or will be after the site goes public, anyways), and the questions are not interesting to most people without graduate-level coursework in math.
MathOverflow is for research level math questions. Math.stackexchange.com is not restricted to any particular level of difficulty (though one expects that it won't get much in the way of research level questions since those are at MO). There was a lot of feeling on SO and MO that it'd be good if there was a site for more elementary math questions.
This site will provide a place for people like myself to become engaged with a broader mathematical community. The questions and contributors at MathOverflow are too advanced for me to answer or contribute useful comments toward.
If there are other people like me, then this site will provide a forum for us to work through problems together, among mathematicians closer to our level.