Everyone is saying roughly the same answer. Some of the answers have been copy pasted but I'll ignore that for now.
SEO in short is a process of ranking up your website for keywords or phrases which results in traffic from organic search engines, mostly Google.
I suggest Googling moz beginner guide. Moz is a top seo news and info site, great little guide for learning how seo works. Say you want to rank for the keyword "strawberry apple donuts."
First you would build your website, making sure you have "strawberry apple donuts" listed in an article or page with a 2-3% density rate. You would want the website to relevant to the keyword so maybe have the website about donuts, fruit donuts, ect. After your onsite has a few nice keywords including the strawberry apple donuts, you would start offsite seo, also known as link building.
Link building requires you to submit links, whether it is web 2.0s, comments, videos, pdfs, article directories, etc with the anchor text as your keywords, naked url, lsi, generic, brand, etc. It's a touchy subject when it comes to anchor diversity and such. This is not a guide, more of an explanation for what seo is. In return, proper seo brings in real traffic.
Remember to check the moz beginner guide. I'm not plugging it, it's just a real good little guide to read, free of course.