The important thing is to make the distinction between your ISP and your website host. Although they can be, they do not necessarily have to be the same. Your ISP (Internet Service Provider) is just that. They provide you with access to the Internet (via dial-up, DSL, T1, etc). Companies such as Comcast, AT&T can be your ISP.
They may also provide you with e-mail addresses and a small amount of free space where you could upload a website. In some cases, this small amount of web space is enough for the personal website owner who wants to put up a small site or show off vacation pictures. It can serve any number of limited prospects. Your ISP may also offer you a web hosting package whereby you may upload a much larger scale site to fit most any need. It is in this example that your ISP and your Hosting Server are one and the same.
Another popular option is to Host your website through another company. You still retain your ISP as a means to access the internet, but an independent host will often give you more space, bandwidth and general options for less money than your ISP could offer you.