Too often, communities are defined in terms of tools rather than actual objectives. You hear about friend lists, sharing photos, posting comments, uploading films, etc. And the main purpose seems to be that you should provide as many tools as possible to make your site "sticky" or "increase pageviews". But you rarely do you hear about why should anyone do any of that. Exactly what purpose is your community serving and how do the tools you make available help the community achieve that purpose?
A statement of purpose should really be the first thing one defines before even looking for a domain name or any technologies. What is it that you want the people that make up the community achieve? What direction should the community take? Having defined that then you must make sure that every tool ("feature") you provide is in aid of that initial purpose and that the users are aware of how you envision the site and its features being used to achieve that purpose.
There are actually two sides to a community statement of purpose reflecting on the one hand the objectives that you or your organisation have in creating a community (personal objectives) and, on the other hand, the objectives for the participants in the community (common objectives). The former may be framed along the lines of "we are creating this community in order to earn money while discussing issues we are passionate about" or "we are creating this community to get feedback about our product" while the latter should be framed along the lines of "this community exists to enable people to share ideas about x" or "this community exists to enable people that like y to connect with each other".
Now, the more personal objectives don't necessarily have to be hidden from public view but that really depends on how closely aligned they are with the more public objectives. There is probably good reason to think that the more closely aligned personal objectives are to public ones the more chances the community has to succeed. For example, if the sole aim is to earn money but the subject discussed is one you as community owners don't care about then make sure you keep that very private. As soon as members realise it, the community will loose credibility. People don't mind that you are in it also for the money - we all need to earn a living - they will, however, not like knowing that you are only pretending to care about a subject they care deeply about.
It's the people, stupid
The next time you get round to designing a community website keep in mind that all you are doing in designing a website is putting together a collection of tools. A community is not a social network, or a forum or a blog. Those are all tools. Facebook, for example, has no real statement of purpose as a community precisely because it is not a community - it is, as they rightly define it, a utility that enables you to create communities. The participants in Facebook then have their own "statements of purpose" and based on those they go about looking for friends or joining/creating groups, etc. Those with a clear idea are likely to be the most successful.

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