Summary
Desire Line or Desire Path refers to an emergence of usage patterns (behavior shown by users) that are different that intended patterns (designed by designer/architect).
By allowing/observing natural usage patterns and allowing the audience to shape the path, designers can embrace the understanding of what a particular design means to users.
A heat map of a website is a great example of the desired path. Users often consume information the way suits them and not necessarily the way the designer intended the information to be used.
Original example
Source: Universal Principles of Design
Online example
Real example
In this picture, a desire line was officially established to the left as a short cut to the parking lot.
Strategy: Desire-line