When people talk about web hosting they usually have in mind the shared web hosting. Shared web hosting is the service which is sufficient for 99% of websites.
Since most websites do not require special server settings and too much server resources it is possible to put several client's websites to a single server. These clients share the server resources (for this reason this type of service is called shared hosting) what cuts down the cost significantly.
If you need to host some complicated script or a website with exceptionally high traffic but do not want to manage your own server then semi-dedicated server is the service you should to check out.
Semi-dedicated server works in the same way as the shared web hosting from the customer's point of view. You will not see any difference - you simply use the control panel to manage your website in the same way as the shared hosting users do. You will not need to care about the server management at all. But in contradistinction to the shared hosting you can use many times more CPU resources and RAM. This makes it possible to run exceptionally resources heavy scripts or websites with millions of page views a day.