Internal linking refers to any links from one page on a domain which lead to another page on that same domain.
This can refer to the main site navigation, like the links you see above this article to our sections on SEO, PPC etc. It also refers to links within articles to related content, such as this link to an article on duplicate content.
An inbound link is a hyperlink on a third-party web page that points to a web page on your site. Inbound links are important for search engine optimization because Google and other search engines see multiple, relevant inbound links to a page as a sign that the content on that page is useful. Basically in order to promote your site you need people talking about your site, so the links that you submit or any mention on any other site that links back to your website makes your site rank better in google.