SEO is short for Search Engine Optimization. SEO may be defined as the art of favorably positioning webpages and websites in organic results of search engines and especially on Google’s SERPs.
SEO consists of ensuring to be indexed by search engine spiders and then to "please" search engine algorithms - mainly Google’s one - to gain good SERP rankings.
SEO is made of on-page SEO and off-page SEO.
On-page SEO consists of optimizing site and page contents through several hundreds of factors. For more details see on-page SEO.
Off-page SEO refers to link-building strategies.
For some websites, traffic gained through SEO can represent the main source of traffic. SEO-driven traffic is often considered as free traffic as search engines are not paid for clicks on organic / naturel results. However, organic traffic is in fact seldom free as websites pay for SEO services or have in-house SEO costs.