The Internet is a vast collection of computers all connected together in one very large network. There are different levels to the network and there are usually many ways to get from one point to another. A diagram of the Internet looks vaguely like a spider web, hence the popular name "the web." A web site is a place on that web, and web site hosting means providing the physical location, the connection and, often, the computer that "serves" the content to whomever requests it. The "servers," or computers, are running special software designed to handle many users and services simultaneously.
Because the Internet is a global network, communication can occur at any time, and it is essential that your "web site" be ready to receive visitors at any moment. That means a constant connection to the web and a server that is always powered on running a stable environment that won't "crash" and need to be reset. The physical environment where the server is located (called the Network Operations Center, or NOC) is also critical: there are temperature controls, backup generators, earthquake-resistant architecture, and more, all designed to ensure your site is available at every moment.
When you create a web page on your computer, you simply transfer the file to the server at your web hosting company. Then, whenever someone requests that file from the Internet either by typing in the address or clicking a link, the server gives them the file they requested. Changing the content is as easy as changing the file and re-transferring it to the server. The most common means of transferring files to a web server is through the File Transfer Protocol, or simply "FTP." Web site hosting, then, also means having an FTP server ready to communicate with your FTP program.
In addition to web and FTP services, web site hosting almost always includes an email server that will receive email sent to your domain (i.e. 24Shells.net). This enables you to control mail delivery, create your own addresses, and present a professional image to your customers, clients, or constituent.