The aim of Silo structuring is to tell search engines that you have large and comprehensive sections of your website devoted to a certain topic.
Google is more likely to rank a page about 'X' if it can see it is on a website with a lot of information related to 'X'. This signal has been shown to be more powerful than backlinks in certain circumstances.
So, for example, lets say on this website I wrote an article about the greatest 100 songs of all time. It might be a very popular page and get a lot of backlinks. But to Google it is completely out of context with the rest of this site.
There is nothing else on here related to music or singers or song writers.
A page with less backlinks but on a website that is (or has a clear section) with lots of other related material is more likely to give visitors a better user experience ... and Google wants people to have awesome user experiences, otherwise they might go and use a different search engine.
Amazon offers one of the easiest to see Silo structures. It uses breadcrumbs which ensure all the pages in a certain area link back to one main page (e.g. everything in 'Home and Kitchen' has a link to the category page 'Home and Kitchen'.
Now look through a product page on Amazon and notice how many links there are to products within that silo or sub silo. Related products, best seller ranking, etc, etc. And so it goes on down through the categories.
Google can see Amazon has a massive silo about 'Home and Kitchen', a pretty huge silo about 'Kitchen & Dining', a substantial silo on Coffee, Tea & Espresso within that, and so on.
If an Internet user is looking for a kettle Google knows they are highly likely to find it on Amazon because it simply has such a huge silo in that area and it will want to rank Amazon because of it ... regardless of backlinks.
The basics are breadcrumbs with structured data markup so Google clearly understands they are breadcrumbs.
Then also look for other opportunities to interlink pages which are related.
I'm Tim Hill, a Search Engine Optimization and Online Marketing specialist. I created this site to help others understand that SEO is not a mysterious black art!.
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