Nested Projects are a way to organize a heirarchy of projects. A Nested Project can have multiple levels or tiers within.
A Nested Project is created in the same manner regular projects are created, with the exception being the initial project contains no boards. So, when creating that first, top level project, simply create the project by entering the project name and image for Step 1, and then skip Step 2 by clicking "Next". Step 3 you can invite team members, and then select "Finish." You have just created your top-level "shell" for the nested projects you create within it.
When you click back into this Project from the Dashboard, you will be presented with an option to create either boards or projects:
Here is where you can start to build your heirarchy of nested projects. By selecting the "Add Project" option here, you may then create projects with boards, all within or "under" the top-level project you created. As well, those projects within may include projects with boards, and so on. Visualize an org chart, and you can visualize the structure of nested projects.
From the dashboard, you'll note the visual cue for nested projects are the layers behind the top layer (whereas regular projects have just one layer). See below:
This visual cue will be apparent at the top level, and at any level underneath that has a nest of projects within.