Definition: Search Engine Optimization (SEO) is the process of optimizing a website's structure and content to get targeted traffic by ranking higher in Search Engine Results Pages (SERPs).
So, how do we explain this in plain English? It all amounts to setting a website in a position to be found by a search engine's ‘spiders' and having a website's content, loading speed and make-up fall in line with that search engine's rules and ranking parameters.
In other words, if Google says you need to do/show/display “X” to be ranked, you do everything you can with your website to make it do/show/display “X”.
Example: if you want your website to rank for ‘Dog Flea Shampoo', you be sure to have content on your website that speaks to Dog Flea Shampoo but, that is not enough. Otherwise, you could just write “Dog Flea Shampoo” all over your site and call it, ‘Good'. Writing about dogs, fleas, shampoo, flea treatments, flea season, etc. all help but ranking does not live on content alone. Also, it must actually be relevant, cognizable content.
Having said that, Google's spiders want to find more than that before deciding that your site deserves to rank higher than others. Spiders want to see:
a fast loading pace of the site;
links between your site and other sites on the topic being ranked;
evidence of ‘authority' on the subject (keyword) from your site and/or from the sites being linked;
Content, content, content! If your site does not speak to the subject/keyword, there is no rationale for Google (or Yahoo, Bing, Yandex, etc.) to rank your site higher;
a positive user experience. The site should be easy to navigate and not be overflowing with ads nor pop-ups;
a site that answers the user's question that is intuited from the keyword entered;
images, videos, etc. must have meta tags that read as relevant to the search topic.
Of course, as noted in the last bullet point, there is more to a website than just text. Yet, for spiders to know whether or not to score your site's ranking higher for, say, images; well, those images would need “tags” that attach to the image in the background ie. the site's computer language that the user does not see. These tags tell the spiders what the image is about and therefore can be identified as valuable or not for ranking.