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 Accurate or not, anything characterized as "legacy" is perceived to be old or outdated (as opposed to a new economy company, for example).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 Supply chain management
A subset of value chain management, it is an old system that's been updated with new technology. It specifically refers to the relationship between a supplier and a retailer. For example, a major retailer can monitor surplus on its shelves right down to an individual product, and this enables the retail store to keep its supplier aware of how its product is selling. In return, the retailer may demand favorable promotions from the supplier.