SEM, or search engine marketing, is when the focus of the marketing effort is around exposure on search engines, whether that be working to improve your websites organic rankings or managing a paid search (also sometimes referred to generically as PPC Marketing) campaign on the search engine. The most common U.S. search engines that are focused on are Google and Bing. These also represent the most active search engines in the U.S. for paid search marketing via their respective platforms for that which are Google AdWords and Bing AdCenter.
Organic SEM represents the more foundational marketing effort, but falls into the long-term marketing strategy versus paid search which can be used as a much more short-term or moment focused SEM vehicle. Essentially, both cross-play very often and should be used in conjunction with each other for the best results overall.