UX, UCD, Usability

What do they mean and why are they important?

I look at these as layers of an onion.

In the center is usability - whether end users can use a product or interface to complete a specific task in a way that is efficient, effective easy to learn, error tolerant and engaging. (Whitney Quesenbery's 3Es)

Next we have user centered design (UCD) which is a methodology which engages users in every phase of a project to ensure that a product is not only usable, but supports users' needs, behaviors and goals.

User experience encompasses all interactions a user has with an organization and the products and services it offers. (NNG)

The one thing that all these concepts share is the central belief that to be successful, you must know your end users, align their needs with your business objectives and integrate their feedback into every phase of product and service design.