Please read this first: The Simplest Online Marketing and SEO Crash Course
SEO means Search Engine Optimization. It's the technique to make your website content friendly to the likes of Google Search Engine. It's a way to optimize and distribute your content or links so that Google thinks that your website has rich content.
Having your website optimized for SEO will get you a load of users that search for your website's keywords. In other worse, SEO is the best way to get you new users consistently without doing any effort (however write a blog entries is quite an effort).
There are different kinds of SEO. One is Online SEO, and one is Offline SEO.
Online SEO means the keywords that you have on your website. This includes the keywords in your URL (the address at the top of your browser), in h1 tags, in your content, in your links, etc.. This also means the keywords used as anchor text to interlink the pages in your own website.
Offline SEO means the links linking back to your website. When other websites link back to your website, they give you link juice. This is kind of like when someone talks about you, it sorta means you're popular. Every website has their own PR (Page Rank - on the scale of 1 to 10), which is the indicator of how much Google trusts that website. If a page with high PR links back to you, then the link juice that that link is able to supply is a lot more than a link from a page with lower PR. 1 link from a PR6 website is worth a few thousand links from websites with PR0-1. Also, the anchor text (the text of the link) matters a lot too, since when Google sees there links linking back to you, they determine your website's content by the anchor text on the links. also see this cartoon explanation!
In short: How I'd like to put it is you can see websites as people. Online SEO is the ability to compliment yourself and not overdoing it. Offline SEO is when people talk about you or refer back to you, while talking about your expertise. When you talk about yourself and a lot of people are talking about you, that makes you a very popular person!
Search Engine Optimization and Tools
SEO and Analytics Tutorials
SEO for Mobile Apps