Shared hosting is web hosting in which the provider houses multiple sites on a single server. For example, Site A shares the same server with Site B, Site C, Site D, and Site E. The upside is that the multiple sites share the server cost, so shared web hosting is generally very inexpensive. In fact, you can find an option for less than $10 per month.
Moving to another website consists of transferring the website’s files and databases, configuring your site with the new host, and directing your domain’s DNS to the new host. Once you pick a new site host, they can usually help you out with this process. The cost will depend on the host you’re switching to, but it will probably be anywhere from $150-$400.