Google traffic section is very important if you have your website indexed by Google. It shows you "landing pages" of visits from google.
This way you are able to see how many visits were there to which pages and what are the most popular pages receiving visits from google
Search traffic includes not just Google, but there are also some other search engines like Yahoo and Bing, but usually they are not that dominating the search engine market just like Google
SEO (Search Engine Optimization) has very important impact on visits you are getting from google. This topic is out of scope of this tool and there are many ways how to improve your ranking in search engines. This section however tells you, how many visitors each page is getting.