Anthropotemry was a way police used to catalog criminals. They would measure different body parts and record the lengths, width, circumference etc. This didn't work well because several people may share the same length of arms or similar nose shape. In addition, those doing the measuring did not always measure accurately which made an even greater overlap in the number of people who would have the same measurements.
The Will West case was the best example of how anthropometry was inaccurate. There were two men, one named Will West and one named William West who had similar facial features. One of the men was previously a criminal and the other was wrongly prosecuted because he had a similar name and similar "measurements" when police checked him out. This case is what led to the use of fingerprinting.
You can find an in-depth story of the Will West case online: http://www.crimescene-forensics.com/History_of_Fingerprints.html