Internet marketing is full of acronyms, but SEO and SEM are two of the most common.
SEO stands for Search Engine Optimization, and is the process of ensuring that your website is doing everything it can to ensure that it is easily searchable and understandable by search engines like Google, Bing, and Yahoo. Websites that do this well come up higher in search results than websites that down.
SEM stands for Search Engine Marketing, and is the process of purchasing paid ads through search engines. These ads are frequently targeted by keyword, region, and more general demographic data.
Both are very important, but SEO is something that should always been done if you want your website to display in searches, and SEM is a process that may or may not be considered based on your marketing goals.