Outreach's goal is to help raise the living standards of more primitive civilizations to the post-scarcity, post-mortality levels that dominate the Mess and the neighboring regions of Puzzlebox.
This involves social engineering, technology transfer, and sometimes less noble methods like brainwashing and meme-war upon less "enlightened" civilizations. Outreach's guiding councils are prone to lengthy, convoluted arguments about the morality of their goals, especially when the more underhanded methods get used.
If you've read Iain M. Banks's "Culture" novels, Outreach is a shameless rip-off of "Contact", complete with a morally-ambiguous "Special Circumstances" division.