User experience refers to how the user of a piece of software (or other system) interacts with and experiences it. A thoughtfully designed user experience can make a huge difference to the reception of a piece of software.
The international standard on the ergonomics of human-system interactions (ISO 9241), defines user experience (UX) as the "user's perceptions and responses that result from the use and/or anticipated use of a system, product, or service." Often, it also encompasses usability.
While user experience design (UXD) is a common consideration in the design and development of much modern commercial software, it is often neglected for scientific software, which may result in software products being less usable then they could be.