Businessmen/bureaucrats/soldiers and the like who follow convention and the company line. Also called just 'suits'.

The literal meaning, i.e. males wearing suits has obviously been part of the language for as long as suits have. The phrase was first used with a specific rather than general meaning to refer to US sports players - the suits being the sporting gear This usage is known since at least the 1930s - for example, this piece from The Ogden Standard-Examiner, April 1933:

"It is expected that around 80 participants will take the field Friday afternoon. Ogden will probably lead the schools with close to 35 men in suits while Davis and Weber, will run between 20 and 25 men apiece."

It isn't clear who first used the term 'men in suits' to describe conventional business people. John Lennon described the people who controlled The Beatles' financial interests as 'men in suits'.