Who is "Greeks (or the Slugs" - Mr. Sergeant Smith, Mrs. Sergeant from The America Play, and Other Works and what is their importance?

Mr. Sergeant Smith is an ambitious army officer, desperate for advancement and approval, which he calls his "Distinction," to the point of being constantly, and deludedly, convinced that it's imminent. Mrs. Sergeant Smith is his wife, focused entirely on propriety and on making sure her children and her husband are perceived in the best possible light. Buffy, Muffy and Duffy are their children, as self-absorbed and as ambitious as their parents and disappointed when neither their father nor their mother turns out to be as heroic and/or as worthy of their admiration as they'd hoped.