There is lots of discussion in the SEO world about whether or not Google uses relevancy of topics and backlinks when determining a site's ranking. Some claim that Google is now using Hilltop in its algorithm. You can read more about Hilltop at https://www.cs.toronto.edu/~georgem/hilltop/. Basically, Hilltop's summary is 'In computing the usefulness of a target page from the hyperlinks pointing to it, we only consider links originating from pages that seem to be experts. Experts in our definition are directories of links pointing to many non-affiliated sites. This is an indication that these pages were created for the purpose of directing users to resources, and hence we regard their opinion as valuable. Additionally, in computing the level of relevance, we require a match between the query and the text on the expert page which qualifies the hyperlink being considered. This ensures that hyperlinks being considered are on the query topic. For further accuracy, we require that at least 2 non-affiliated experts point to the returned page with relevant qualifying text describing their linkage. The result of the steps described above is to generate a listing of pages that are highly relevant to the user's query and of high quality.'
Other SEO's point to TPSR (Topic Sensitive Page Rank) as the new strategy that Google is using. TPSR focuses on a pre-determination of specific topics and setting a Topic Sensitive PageRank for those topics. Then, this new type of pagerank is used in conjunction with regular PageRank to help determine SERPs ranking. You can read more about it at https://www2002.org/CDROM/refereed/127/.
Still others can point to sites that do NOT have many relevant backlinks, and yet those sites still do well in the SERPs.
My theory is that we may never know exactly what Google's algorithm is based upon, but we can use common sense in optimizing. Does it make sense to get backlinks from on-topic, relevant directories? Of course it does. Does it make sense that those links should have relevant anchor text? Certainly. Does it make sense to be linked to from sites that you would consider to be authorities on the subject matter? Yes. Does it make sense that your on-page optimization should reflect the relevancy of the topic? Duh, of course. These are all just common sense things that if applied, would naturally imply that your page is worthy of a good ranking. Do what makes sense - and you should do well.