Trello comes from the folks who make the excellent Q&A group of sites originating with Stack Overflow, and as the developers put it, it's simply "a web page where you make a bunch of lists". Making those lists is incredibly easy; you create a project, add cards to it, and add list items to those cards. If that's all you want from the site (and that aspect is solid enough that you might be satisfied with it for simple list making), you'll be happy. But Trello starts to shine when you dip your toe into collaboration.
To collaborate, you invite people to join your "board" (a board is like a project). Once they join, you can then drag people to items within your project to keep track of who's working on what (that's one of the main problems with collaboration Trello aims to solve). Click on any individual list item and you can add comments, add checklist for tracking progress on that task, attach files, and more.
The whole site's very user friendly, and that combined with the depth of functionality make it a strong solution for people looking for anything ranging from simple list-making to full-on team management and project collaboration.