Longman Dictionary of Contemporary English
Wiktionary
n. (context business English) A method of management in which instructions are passed to and from one's superior
WordNet
n. administration of the line functions of an organization; administration of activities contributing directly to the organization's output
Wikipedia
Line management is a business term to describe the administration of activities that contribute directly to the output of products or services. In a corporate hierarchy, a line manager holds authority in a vertical (chain of command), and/or over a particular product line. He or she is charged with meeting corporate objectives in a specific functional area or line of business.
As an example, one type of line management at an automobile conglomerate might be the "light truck division", or even more specifically, the "light truck marketing line". Similarly, one type of line management at a financial services firm might be "retention marketing" or "state municipal bond funds".