The practice of User Experience (UX) Design is the coming together of many specific design related disciplines to improve the usability, responsiveness, uptake and aesthetics of a product or service.
UX Design is carried out by anyone involved in designing an app, service, website or product, who contributes to the design in a way that will improve the user experience. UX Design teams may be made up of many disciplines including; user interface designers, information architects, product designers, developers, engineers, business analysts, project managers, researchers, copywriters and more. The specific roles and responsibilities will vary greatly and multiple roles can be covered by a single person.
Every experience that must be designed goes through some process of user experience design. Designing a good user experience takes research, planning, deployment, testing, and iteration.
User Experience Design as a profession cannot be well defined as it is not a (single) discipline, talking about UX Design as a profession narrows it to something less than what it really is. UX is perceived in many different ways and is sometimes used as a buzzword for usability, user-interface, wireframing or any other number of disciplines or tasks.
It has become a catch-all phrase an individual or agency (including ourselves) may use to convey the gamut of abilities they employ to deliver a design that is considerate of its target users experiences.
An interesting analogy about what a User Experience designer does:
User experience design