What does it mean if your stool looks greasy?

Incomplete digestion. Aside from dietary extreems, this represents a serious problem in your intestines. Please check in with your doc.
Greasy stool? Are you seeing oily stools with floating oil droplets (which implies fat maldigestion from use of dietary fat blockers, pancreatic and/or biliary disease, small bowel malabsorption, or excessive dietary fat intake) or mucusy stool (due to a range of conditions from inflammatory, infectious, ischemic, or "functional" due to rectal dysfunction, colon delay, or irritable bowel syndrome)? Need tests.
Fat malabsorption. Greasy stools, unless taking mineral oil, generally means poor digestion of fats. Can be seen with pancreatic problems, and/or small intestinal problems like celiac sprue, parasitic illnesses like giardia, other GI problems. Needs to be seen and evaluated. See your doc.