The terms are usually used in the context of data centers.
Generally speaking, "east-west" traffic refers to traffic within a data center -- i.e. server to server traffic. "North-south" traffic is client to server traffic, between the data center and the rest of the network (anything outside the data center).
I believe the terms have come into use from the way network diagrams are typically drawn, with servers or access switches spread out horizontally, and external connections at the top or bottom.