An inbound link is a hyperlink from another website. The Internet is designed to allow authors to link (provide a way for users to click through and be taken automatically by their browser to the destination page or information) to other resources. If an author, user or automated feed reader places a link on a site which points to a resource or page on your site then it would be said you have earned an inbound link.
These have always been one of the most important factors for Google and other search engines when ranking pages as they are an indication of other users finding the information useful and of a high enough quality to point other users to. This does lead to some abuse of the system and search engines now have to be mindful of marketers paying for or using some spam-like techniques to obtain a higher number of links. The rank of the site linking is becoming increasingly important so an inbound link from a very important site such as the New York Times would be a lot more valuable than from Bill’s Plumbing Blog!.