What is it?
Search Engine Optimization is using both on-site and off-site techniques to increase a website's ranking in the search results for the resulting increase in traffic.
There are lots of strategies - varying from white-hat to black-hat - to help a website rank better. Most of the strategies will fit within five basic categories:
Keyword research - Researching keywords for each page, paying attention to search volume, the amount and quality of competition and the likelihood of ranking for those words and phrases. However overusing keywords can lead to a penalty. The trick is using them enough so visitors and search engines know what the page is about, without using them so much the text sounds unnatural.
On-page optimization - Writing content specific to those keywords, including using those words and phrases in particular places on the page, but not overdoing their usage.
Site technology - Ensuring the website and page structures are optimized for both visitors and search engines. These include how fast the page loads, whether there are header tags and a page description and whether the page can even be found within the website.
Social media marketing - Sharing content and growing the website's visibility in social media to increase brand awareness and increase social signals. Greater visibility of good content increases the chance more people will find it and link to it.
Building backlinks - Encouraging people to link back to content on another website. Building backlinks has been the focus of SEO for many years, but the popularity led to unnatural link building which often leads to penalties.
Here are some resources if you'd like to learn more ...