Fingerprint function is a crystal structure descriptor, a 1D-function related to the pair correlation function and diffraction patterns.
It does not depend on absolute atomic coordinates, but only on interatomic distances.
Small deviations in atomic positions will influence fingerprints only slightly.
Fingerprint theory (Oganov & Valle, 2009) allows quantification of the degree of order and complexity of a crystal structure.
One could also measure the similarity between structures.
For more information about this function, you can check the main references:
1) Oganov A.R., Valle M. (2009), How to quantify energy landscapes of solids, J. Chem. Phys. 130, 104504 (pdf).
2) Lyakhov A.O., Oganov A.R., Valle M. (2010), How to predict very large and complex crystal structures, Comp. Phys. Comm. 181, 1623-1632 (pdf).
3) Valle M., Oganov A.R. (2010), Crystal fingerprints space. A novel paradigm to study crystal structures sets, Acta Cryst. A66, 507-517 (pdf).