Epic
A very large user story that is eventually broken down into smaller stories; epics are often used as placeholders for new ideas. Epic cuts across various features of a product and may span across multiple releases.
For instance, an Epic can be ‘Optimizing Customer Service’.
Features
A large user story tied to an Epic (created in order to achieve a particular goal of the Epic), targeted at a specific product function. Usually fits in a release.
For instance, Case Management for Servicing Team, Self-Service for the Customers, Self-Service Knowledge Base can be the different features for the above mentioned Epic.
User Stories
Smaller pieces of functionality, directly mapping to the Feature, but small enough to fit in a sprint.
For instance, the ability for a service representative to create a case can be a user story tagged to the feature ‘Case Management for servicing team’.