There were two main factors driving us to incorporate:

1. We're going to host Wikimania 2012 here in DC.  Organizing a conference of this scale requires a very large sum of money.  Handling this money safely requires a corporation (or, to be more precise, a limited liability entity, of which a corporation is the most common form); otherwise, the individual Wikimedians who participate in the Wikimania planning could potentially wind up being liable for the costs of the conference if anything goes wrong.  Further, raising this much money will require donations, which again requires a suitable entity (i.e. a 501(c)(3) non-profit corporation) to receive the funds; nobody is going to give $50K to a random Wikimedian.

2. More-or-less separately from this, the idea of becoming a Wikimedia "chapter" has been in the works for a long time, mostly in relation to GLAM outreach and so forth.  Getting chapter recognition again requires a corporate entity of some sort that can sign the relevant trademark agreements with the WMF; the WMF has specified that this entity should ideally be a member corporation.

Basically, we're forced to incorporate as a non-profit if we want to make any real headway on either issue.  

The formality is really just a consequence of having to go through the necessary legal and procedural steps to (a) set up a corporation and (b) operate the corporation in a way that doesn't leave its members/directors/etc. personally liable.

Kirill