Custom templates are unique view layers which can be made for any type of block in a concrete5 install. A custom template is an actual PHP file, each block type has a directory for them.
When you are in edit mode for a page, you can choose to set a custom template for a block. You will be presented with a list of available custom templates for this block type.
Custom templates are used to change the presentation for the data a block presents.
The Auto-Nav block is a great place to start when thinking about custom templates. The Auto-Nav block brings back part of the site tree you define with settings. 
On its own, it always displays the results as an Un-Ordered list in HTML. This is pretty common practice these days because you can do a lot of styling with these lists. Without any further work, a new Auto-Nav on your site would look like the image to the right.
There are several custom templates that come with your Auto-Nav block. If we choose the Header Menu custom template for this instance of the Auto-Nav block, it will look something more like this:
Same pages, and yes some CSS styling, but also a bit of PHP logic used to determine which page if any is active and put a box around it. Custom templates are view layers for blocks.