It's mostly a matter of preference. If you are used to something like Wordpress where you have a concept of a header and footer that you include into pages than you might not like layouts. I personally only use layouts with content blocks because the non-layout way tends to cause more repetition.
As for partials vs blocks. You use a partial for items that you want to reuse on different pages. While a block is a chunk of html that will be replaced by child templates.
An example of a partial can be the html for a product. So you have a thumbnail, the title and a description of a product. You might use this partial while listing the products in a category. But you might also use this partial for rendering a list of search results.
An example of a partial can be a main layout that contains you header and your navigation and a content area. If you want to reuse this main layout on multiple pages you will extend this it and overwrite the block in the child templates.