SEO is done to improve your SERPs, the position at search engine and link building is one of the most important factor in SEO
Backlinks are incoming links to a website or web page. search engine optimization, the process of increasing the amount of visitors to a Web site by ranking high in the search results of a search engine.
SEO means building your content to get placed high in the search engines. Things like writing unique content and using you keywords often without sounding spammy. Backlinks are links on other sites leading to yours or a "vote" for your site.
Linkbuilding (creating backlinks) is part of SEO. There are many, many aspects to SEO. Linkbuilding is just one part, albeit significant.
SEO is a technique of increasing traffic, visibility on SERPs, Conversion rates and ROI. It include both on-page and off-page. Backlink is a part of off-page SEO technique.
Ditto @Peace4ever9: If you're still confused read this... http://guides.seomoz.org/beginners-guide-to-search-engine-optimization