In geology, a foliation is a crude layering of rocks produced under compression. The layering is approximately parallel to the bisecting planes of folds, and often results in the rock splitting because of the parallel orientation of the mineral layers. Mica and slate are good examples of foliation.
In topology, a foliation is a decoration of a manifold in which the manifold is partitioned into sheets of some lower dimension, and the sheets are locally parallel. More technically, the foliated manifold is locally homeomorphic to a vector space decorated by co-sets of a subspace.