Backlinks are links that are directed towards your website. Also, knows as Inbound links (IBL's). The number of backlinks is an indication of the popularity or importance of that website. Backlinks are important for SEO because of some search engines, especially Google, will give more credit to websites that have a good number of quality backlinks, and consider those websites more relevant than others in their results pages for a search query.
Outbound links are links that point to some other domain from your site. When you link out to related domains, it not only helps the search engine to understand your niche but also helps to increase the trust and quality of your site which plays a vital role in your blog's SEO.