To make a long story short, projects were pitched to an idea board, and were up or down-voted on by community members. Ideas that got traction were "green-lit", which basically meant that the Assembly company would provide resources for it like hosting, DNS, email services, git repositories, etc., etc.
Apps that were greenlit could create bounties for work that needed to be performed, and any member of the community could collect on those bounties. Need design work like logos and icons? A designer (or many designers) could grab the work and submit their entries. Each unit of work would be awarded a pre-determined amount, and those payments amounted to a blockchain allocation -- e.g., submitting a logo might be worth 100 points, while submitting the accepted logo might be worth 1,000 points. That 1,000 points equated to ownership. If there were 10,000 points awarded to date, your 1,000 points were worth 10% ownership.
If the product was developed, completed, marketed, etc., and turned a profit, Assembly would collect a rake to cover expenses, and all the profits were paid out based on allocation.
It was a good system, really, and resulted in some pretty neat projects. That said, I'm not surprised to see it being shuttered. A while back they pivoted most of their tools into being some kind of community changelog, and as a fairly active participant, I literally stopped using it after that, as I had no idea how to use it, saw no instructions, and all the chatrooms that had existed previously had been shuttered in favor of the changelog.
I assume, but have no inside knowledge, that between participation dropoff, and the other end -- that many projects were either never completed, never marketed, never got traction, or not really good, they were outlaying too much and getting too little success on the other end.
For a (probably) better description of what they were, this article is handy: http://tech.co/assembly-basically-group-projects-adults-2015...