They say no two fingerprints are the same. Even identical twins (who have the same DNA) will have different fingerprints. Fingerprints make it easy to identify a person, if prints have been left at a scene. And if the police have anything to compare it to.
As far back as 1686 an anatomy professor at the University of Bologna, Marcello Malpighi, noted the spirals, ridges and loops in fingerprints. He did not mention anything about their value in identifying people. Jump ahead to 1823 and another anatomy professor, John Evangelist Purkinje, from the University of Breslau, discussed nine fingerprint patterns in his thesis. He too did not mention their use in identifying individuals. However in the later 1850s people used their fingerprints as signatures or part of their signature. Finally, in 1888 Sir Francis Galton put ridge and loop together and thought fingerprints could be used as a means to identify people. Then in 1892 Juan Vucetich made the first criminal identification of a suspect. A bloody print was left at a crime scene and he was able to identify Francis Rojas as the murderer.
Now of course we use fingerprints all the time. They can even get partial matches. They use powder and a dusting brush to collect visible fingerprints left on soft surface. But they can also use superglue fuming for prints on non-absorbent surfaces. Fingerprints are kept in a database that law enforcement can use to compare prints found at crime scenes.