The User Interface describes the interface that the user interacts with when using an application, visiting your website, etc. The User interface includes your toolbar, buttons, windows, and anything (visual and audio elements) on the webpage that the user can interact with. The key to a website that will retain visitors has a clean, easy-to-use UI. Make all of your links easy to get to, and make sure that nothing on your interface is hard to look at. The more intuitive your interface is the less likely you are to have visitors leave after seeing a single page.
The User Interface is the conduit on a display that allows a human to interact with a computer more easily. Good UI should be fluid and easy for most people to understand.