The expression "men in grey suits" or "grey suits" usually refers to powerful people who operate behind the scenes. This phrase is often used to describe faceless and almost secretive people who control politics, business, or other important matters without attracting attention to themselves. The expression is usually meant to evoke suspicion or fear of puppet masters who pull the strings anonymously and without any accountability.
Over the years, as feminist ideas have influenced language, men in grey suits have became, simply, grey suits. A grey suit may be the officer at the bank who denies a loan, or a government official who announces a change in the tax law that benefits only the very rich. Over time, it became less and less necessary for them to wear grey. The current generation of suits have become not only sexless and faceless, but bodiless to the point where they are ever-present ghosts with no physical presence.
Suits, because of they are associated with formal dress and uniformity, are often symbols of power. They are also often associated with people who have enough money to dress well. Because of these associations, a suit is often used as a metaphor for a faceless authority figure, usually with money. In this context person may be referred to simply as "a suit," usually derisively.
The expression men in grey suits may have its origins in the mid 20th century when the post-World War II generation came of age and rebelled against the social and political norms of their parents' generation. In the United States in particular, flower children, hippies, and other baby boomer adolescents often rejected their parents' ideas about proper dress. The younger generation favored jeans and casual clothes over the more formal attire their parents believed was appropriate. The older generation, and its authority figures, therefore, were suits because they wore suits while younger people rejected that generation's dress codes.