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 Legacy business
Slang for a traditional brick-and-mortar firm. Accurate or not, anything characterized as "legacy" is perceived to be old or outdated (as opposed to a new economy company, for example).