User Experience Design is a process aimed at creating a product or interface for varying types of people with the consideration of their capabilities, expectations, assumptions, and objectives.
From Wikipedia:
User experience design (UXD or UED) is the process of enhancing user satisfaction by improving the usability, accessibility, and pleasure provided in the interaction between the user and the product. User experience design encompasses traditional human–computer interaction (HCI) design, and extends it by addressing all aspects of a product or service as perceived by users.
In other words it’s a design methodology intended to create a design from a holistic perspective, viewed from the eyes of the end user. We answer questions like can a user accomplish task x on our website? If they are—how easily are they able to accomplish the goal? Are they frustrated by the experience or are the neutral or aggravated?
These are important questions to answer when designing a website. Often times the business objectives don’t always line up one-to-one with the end user. In these cases we need to identify a solution that meets the needs of both parties and we fall back on a user experience design process to help identify possible options and test their validity.