Permission marketing is a term popularized by Seth Godin, whereby marketers obtain permission before advancing to the next step in the purchasing process. For example, asking permission to send email newsletters to prospective customers. It is mostly used by online marketers, notably email and search marketers, as well as certain direct marketers who send a catalog in response to a request.
On this site, See opt-in.
For a very thorough history see this article on Wikipedia.org