In modern usage, effigy most often refers to a likeness, such as a dummy, that is hanged, burned, or otherwise abused when protesting the despised person's actions.
If you've encountered the phrase "in effigy,” it's probably been in a news report about protesters burning a stuffed figure made to look like a loathed corporate leader or head of state. Since the 18th century or longer, effigies have been destroyed in place of individuals who, as far as the angry crowd is concerned, have escaped justice. Effigy can also refer to a sculptural portrait of the deceased reclining upon a burial monument.