The concept is really simple. Google answers your questions. Your question (word or phase) is known as a "keyword" in SEO lingo.
Google's business model rests on providing highly relevant answers to all the possible questions that anyone could ever ask. In order to do this, Google uses incredibly sophisticated technology. For every possible keyword, Google calculates a ranking of the most relevant webpages on the entire world wide web. This ranking forms the search results for each given question*.
Coming around to your question, if someone types a keyword and then clicks on your site from the search results (not the ads), it's called "organic" traffic. So there is no such thing as "organic SEO", because all SEO is organic. The definition of SEO is optimising your site such that it appears high in the organic results of the particular set of keywords that you have decided are relevant to your business.
The other side of the SEO coin is PPC (Pay Per Click) where you pay for an ad that drives clicks to your website.
So in answer to your question, if you pay for your traffic it has no direct influence at all on your organic search ranking. However, if you drive people to relevant content, and they start to share or link to that content, it can have an effect on your organic ranking.
In conclusion, you do PPC to start the fire and SEO to keep it burning...
In the past, the Google bot was quite dumb, so there were ways to trick it. This is known as "black Hat SEO" – it's where a lot of the mystique and misinformation around SEO originates from. But in 2017, such techniques are only relevant if you plan to keep a business only for a few months (before creating another one etc.) – 99% of businesses don't operate that way.
* – In fact, Google's technology is even more mind boggling as the results are also personalised depending on who is asking the question!
The social sharing might help a bit, these days Google is using more and more AI to figure out relevance. The other change Google is making is more and more personalised searches. So keep in mind that your site will probably rank higher in YOUR search results than in other people’s.
The way to start with SEO is to make a short list of questions (keywords) that people might ask Google if they were trying to reach one of your pages. Then you produce content to answer the questions (i.e. you include the keywords in your article or product description in a natural manner). Do this for each page of your site. Once you have the content set up, you have to get trusted and relevant 3rd party sites to link to your pages.
The most common newbie mistake is attempting to rank for keywords that are too competitive. For example, “buy books online” will return a list of long established and trusted book retailers that you’ll likely never outrank as a new business. If, on the other hand, you’re in a very niche business, it could be very easy to rank highly without doing anything special and with a bit of care you could easily reach no. 1.
Bottom line, if your content deserves to be ranked highly by being the best answer to the user’s question, it will be. ;-)
Shopify is good for SEO but there are some duplicate content issues which can hamper your performance in the search engines. Fortunately we've created an app to tackle these issues. Check it out here: https://apps.shopify.com/sitemap-noindex-manager
I want to give my own take on something Andrew said. This is based on Brian Dean and other experts.
He said "However, if you drive people to relevant content, and they start to share or link to that content, it can have an effect on your organic ranking."
I would say it this way, if you get X amount of organic traffic and that traffic stays on your page, engages with your page (time on page) for some time, then Google has determined that user had a good experience and got a very relevant search result. Therefore Google will bump you in the search rankings. That has been proven by Brian Dean and Rand Fishkin, fyi.
When Andrew went on to say that they share or link to your content, that's just off-page SEO, and that is a regular part of Google ranking factors (mostly the relevant, quality backlinks) that increase your rank.