In the area of chemoinformatice, in order to discover new types of chemical to address some disease one approach is to associate members of a large chemical database with some coordinate space and consider those chemicals which fall in some sense close to known useful pharmaceuticals. (As a simple example, let's say molecular weight along one axis, polarizability along another, number of hydrogen bond donors/acceptors, rotatable bonds, radius of gyration, and perhaps hundreds more) But there are problems with such a high dimensional space[1] particularly if one wants to do some useful statistics, cluster analysis, etc. So enter PCA as a means to lower the dimensionality to something more tractable. At the same time it gives you eigenvalues with a sense of what your target "cares" about among known chemical descriptors (low variability along one axis might indicate relative importance) versus physical factors with more permissible variation.

[1] https://en.wikipedia.org/wiki/Curse_of_dimensionality