You can configure the way your products are displayed at the main Products page. Please find the following buttons and fields at the end of Products Toolbar:

You can adjust columns width by clicking on the first icon. Second and third icons expand and collapse products when "Show all grouped" Filter is chosen. You can make your own filter or use "Filter by selected category" option (see picture below).

Filter option is actually the one that is responsible for the products' view on the page. You can select from two filter types, specified in a drop-down:

Filter by Selected Category

You can see all the products from the category you've selected in the Categories section. No additional sorting options are available, only standard column sorting.

Show all Grouped

You can see all the products that belong to all categories. The first special feature of this filter type is that a Category column is added to Products section. You can also see a grey box at the top of all columns that says: "Drag a column header here to group by that column".

Whenever you drag any column header there (Category header grouping is shown below), products will be grouped in categories by this selection:

You can Expand/Collapse any category by double-clicking on it. When any category is opened, you'll be able to see full product description. You can also use Expand  / Collapse  products buttons at the main Products tool-bar.

There's also a possibility to build a "category tree" using this filter type. Let's say you want all your products grouped by Category and each Category by different Price. Than simply drag Price header into the grey field and drop it behind Category Field. You can also set "Category" as a category with "Price" subcategory; just drop Category ahead of Price Field.

When you drag column header back it would be placed between the columns where you droped it.