Epic:   A very large user story that is eventually broken down into smaller stories.

User story: A very high-level definition of a requirement, containing just enough information so that the developers can produce a reasonable estimate of the effort to implement it.

http://www.telerik.com/agile-project-management-tools/agile-resources/vocabulary.aspx

Feature: A distinguishing characteristic or capability of a software application or library (e.g., performance, portability, or functionality).

http://en.wikipedia.org/wiki/Software_feature

Relationship between user story, feature, and epic?
I was taught that if you want to change the direction of a three phase rotating machine that is rotating in forward direction, you interchange the phases. Since the phases has the same features (voltage and current), what is responsible for making the machine to rotate in reverse direction, when the phases are interchanged?
