To give you a real example, I recently talked with the founder of Neovim who chose Waffle to manage their large open source project (https://waffle.io/blog/2014/04/17/open-source-spotlight-neov...). The main reason they used Waffle over Trello was the integration with GitHub Issues (the Trello-Github integration options aren't great, and there's difficulty around trying to get people to update the status of work in a tool that doesn't tightly integrate with all of GitHub's Issues, commits, PR's, etc.)
As a recent comment suggests it's a "kanban board".
if this is a valid use case, how does this really differ from something like Github issues or a public Trello board?
comparing https://waffle.io/waffleio/waffle.io to https://trello.com/b/nC8QJJoZ/trello-development i'm having trouble differentiating.