An Internet Service Provider (ISP) is the company that sits in between the Internet and someone that wants to use the Internet. These companies are often the phone or cable companies themselves, but sometimes they are independent providers of Internet access. Of course, if they're independent vendors they still need to work with the phone and cable companies since they are the ones that have the communications infrastructure.
Originally, ISPs required users to dial in much the same way that you dialed a phone. However, over the last several years it has become more common for connections to be always on or to at least require only a second or two to be established.
At the consumer level, ISPs provide Internet access along with basic services such as e-mail accounts, spam filtering, and sometimes antivirus software. At the corporate level, ISPs provide a guaranteed level of service, configuration flexibility, and a lot of bandwidth. As you can imaging, corporations pay much more than consumers.