Scut work is a derogatory term used to describe the non-teaching labor that medical students and junior residents must do in order to be "part of the team". For example, running down labs/xrays, changing dressing, starting IV lines, writing notes, and a whole lot of other stuff that really teaches you little medicine, but is a lot of busy work. The "Scut Monkey" (scut doggy, scut puppy) is used to help alleviate some of the busy work for senior doctors so that they can do more "important" things.
Some hospitals are notorious for scutting their students and residents to death, while others have so many ancilllary services (ie. IV teams) that the student or resident never get any hands on experience for procedures. Somewhere is the middle lies a perfect balance where students and residents gain practical experience without being bogged down with extra labor.