What Legacy business is
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 Accurate or not, anything characterized as "legacy" is perceived to be old or outdated (as opposed to a new economy company, for example).
The meaning of B2G (Business-to-Government)
An acronym that describes business-to-government relationships. With the government being the largest employer in the U.S., B2G is expected to become big business.