Servers are basically very fast computers connected to the Internet on a fast connection network and runs softwares which ‘serves’ your files to the requester (browser). Before starting with the hunt for the right host, you must prepare a list of your own requirements depending upon the nature of site. A business site will need more features and demand more resources as compared to personal site.
Some of the things to check are required disk space, bandwidth, and ability to host multiple domains, tools to generate stats, mail facility and backup. Also if you want to go for Windows based hosting (needed for ASP, DotNET, MS-Access) or the more popular linux hosting. Also take into consideration the Data Center location, and the server specifications as they go a long way in ordinary and exceptional hosting.