From an end user's perspective, the user interface (UI) is the software. Whatever amazing algorithms or data manipulation your program is doing behind the scenes is irrelevant to them; they take it for granted that your software does something. What they care about is how they can use it.
A good user interface makes a user feel in control. When they feel in control they are happy and productive. What this means is that not only must your interface do something; it must also make it easy to do it. If the rise and prevalence of Apple products shows anything, it is that design matters as much as function. Apple didn’t invent the mp3 player- they just made the first one that everyone wanted. That is the power of good user interface design.
When we design an interface we are constantly seeking to streamline the user experience. This means making processes take fewer mouse clicks to complete, supplying input mechanisms that don't let the user make mistakes and designing layouts with a visual hierarchy in line with the goals of the software's functionality.
User interface can extend beyond the realm of graphic design as well, and can involve things like an accelerometer, a GPS, voice recognition, or even a camera that analyzes your gestures. When creating a user interface, we always consider the medium and if there are opportunities to create an innovative interface that can make the software interface more efficient and effective.