A trench was a man-made ditch used in warfare. The digging of trenches could be a form of punishment.
In 2370, Li Nalas described himself as better at fighting in the trenches (i.e. do the actual fighting) than holding the high office of navarch. (DS9: "The Circle")
Later that year, Odo warned Quark that if he tried to sell a small cloaking device, he intended to insure that the Ferengi spent the next 50 years digging trenches in a penal colony. (DS9: "Profit and Loss")
In 2375, after Kathryn Janeway noted that Captain Rudolph Ransom's crew called him by his first name, he described the lack of formalities on the marooned USS Equinox, noting that, "When you've been in the trenches as long as we have, rank and protocol are luxuries." (VOY: "Equinox")