What are Projects for?

Firstly, Projects in Toolbox aren't necessarily "Projects".  While they can be used to plan and manage tasks for small projects, they can be used for so much more. 

Projects can be used to provide a 'window' into the system to quickly see content associated with a branch location, a department, a division, a major project - or any other grouping that's useful to you. You might even create an 'onboarding' project to show new employees the essential content they need to get going in your company. 
Everything in Toolbox can be linked to a Project (or more than one), and you can view all of that linked content by clicking on the project title - either in the list of projects under 'Projects' in the top bar, or in any content item linked to that project.
When you're looking at a project you can see the various modules, pre-filtered by the project. Creating a new item (e.g. an Issue, a document, etc) from this project view, will automatically link it to this project. 
Here's a view of all the issues associated with this location:
You can see that you still have all the search & reporting capabilities available - with everything filtered to only show information relevant to this location.