What E-business is
Any business that is deriving revenue at least in part from something "electronic," usually on the Internet. It also refers to a strategy or service that enables a business to do more business because of Internet-related technology (see: Cisco, for example). The tendency for companies to put an "e" in front of a new product or service primarily comes from marketing departments that are trying to convince consumers they have an online strategy. The traditional brick-and-mortar firms that are starting an online component will use this marketing term to announce they are now online.
The meaning of Commerce
In general it means to conduct transactions online. It is considered a technological term because any kind of commerce conducted online requires a technological application behind it. From a marketing point-of-view, commerce is discussed with reference to the three big C's: content, commerce, and community. These are thought to be the three components driving the new economy.