Tasks/projects in your day or from a smart list can be grouped by category in various ways.  Each of these groupings requires the Category/Project Sections strategy to be on.
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When you group by Main Category, your tasks and projects will be grouped based on which Main (i.e. top-level) category they are in.  This is the left-most column in your Master List:

So each of these categories contain one or more of the tasks being displayed will show as a section:
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Grouping by secondary category is similar to grouping by main category, except that secondary categories (the children of your main categories) are shown.

In the above example, Fitness and Diet are secondary categories.  So when the above tasks are grouped by secondary category, we see the following:

Notice that "Test blood" is shown in the Health category, which is a main category, since it's a direct child of Health.  So grouping by secondary category really means: group by secondary category when possible, but otherwise group by first category.  In practice you'll probably use "Group by secondary category" in situations where all the tasks/projects you're sectioning live within a secondary/tertiary/etc. category.
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All of the above applies to grouping by tertiary categories, which are the children of your secondary categories.

Gym and Fitness are tertiary categories in the above example.

Grouping by category allows you to group by the most immediate parent category, whether it be a main, secondary, tertiary, quarternary, etc. category.
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In the above example, both "Test push notifications" and "Test notes on Android" would be put into a Mobile section.  There wouldn't be a section for "New Note Editor" since it is a project, not a category:

Grouping by project works the same as grouping by category, except that the most immediate parent project is used as a section.

As expected, "Test notes on Android" goes in a section for the "New Note Editor" project, whereas "Test push notifications" is put into "None" since it doesn't live in any project.

Grouping by project groups items into their most immediate parent, be it a category or project:

Grouping by next level is only available when you are looking at a project/category in your main view.  This can be accomplished by clicking on a Category in the sidebar Categories section, or by clicking a sidebar/bottom menu/custom square/custom text link item with type Category:

Without any grouping you will see the normal tree view for the selected category:

Now group by next level is available:

and it expands those categories into sections:

So we're viewing a main category, Health.  And its children are expanded as sections.  That's the next level.  Similarly, if you click "Fitness" in the sidebar and group it by next level, its children will be the sections:
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