SEM is the marketing process with a goal of getting more visibility in search engines either by getting more free traffic (SEO) or paid traffic (Paid search advertising).
Through paid search advertising you essentially buy advertising space in the search engine results. So instead of trying to rank higher and get free traffic you pay to appear in front of the searches.
The most well-known advertising agency for PSA is Google Adwords. Through Google adwords you can get your ads appear in the Google search results and you pay only for the clicks on your ads. This is also the reason why the whole process is called Pay-per-click or PPC. Bing and Yahoo have a similar system but it not so successful and widely known as Adwords.