The process of breaking user stories down into (a) smaller, more easily implemented user stories or (b) tasks. Likewise, epics may be decomposed into user stories, and tasks may be decomposed into more fine-grained tasks.
Story splitting is usually performed during backlog refinement and sprint planning. It is an important precursor to story sizing (estimation). Story splitting may also occur throughout the development process.
In the typical product backlog, user stories grow more fine grained as they near implementation and are larger and less detailed the further down the queue they reside.
Quick Reference Guide for Splitting User Stories – Agile Learning Labs – blog post, PDF
SPIDR: An Alternative Method for Splitting User Stories – Ascendle – blog post
How To Split A User Story? – Vibhor Chandel – Video (19 minutes)
Five Story-Splitting Mistakes and How to Stop Making Them – Mountain Goat Software – blog post