SEO is Search Engine Optimization, as you rightly pointed out. All it does is to make sure that your work on the web is visible to search engines (via their bots). If the work is visible to search engines, it crawls it (essentially making a copy of the text content), and then ranks it against other sources having similar content, using complex algorithms (which is primarily a reason Google is what it is today). Then when a visitor, a user search the search engine for a text he/she would like to search about, the search engine takes these texts as "keywords" and runs it against its database of content that was collected by the crawlers. Then based on the search keywords, and the list it prepared by ranking using the algorithm, it lists the results in what is called SERP's (Search Engine Result Pages). The highest ranked (as per the content relevance) by the search engine's algorithm shows in the first place and so on. There's an exception here. There are times when a couple of posts are shown at top, a bit differently. These are sponsored posts, which are there because Google is paid by the respective owners to show it in their SERP's. This is because of Google's AdWords, where marketers pay Google to show their ads in their search engines and other products which includes Gmail.
Now how can SEO optimization work for your blog?
Read the keywords thing and the user searching for these keywords. A site/blog with better SEO Optimization, better keywords, and relevant content tends to be shown up in the search results. Also, if there is something unique about your blog, there are chances the search results will give less results and your blog might end up being on the top.
PS. This is what I understand about SEO. Professionals might have a different take. So this is not the last word on SEO.