ChicagoKarl points out an article at FAZ that tries to explain in English the German concept of a Spießer, which can't really be explained. LEO says it's "bourgeois" or "square", but that doesn't really cut it. It's more of a middle-class, middle-aged conformist. You could also say suburban, except Germany doesn't have suburbs.
My personal definition is "that what we once ridiculed, but what we have now become", which I usually think of when I'm mowing the lawn, even though I'm allergic to grass clippings and don't really care how the lawn looks.