User Interface is the point of contact between the person or people using an application or system and the system itself.
User Interface is usually considered under the rubric of Human Computer Interaction which is considered a subdiscipline of computer science and is usually divided into the following categories.
Graphic Design (where it intersects)
Usability (see Software Usability)
Graphic Design can be abused; it is a subset of interface design
Graphic Design is hardly a "subset of interface design". There is an intersection. The visual languages that make movies, magazines, and even roadsigns "work" have nothing (and everything) to do with User Interface.
Some resources:
Bruce Tognazzini's site www.asktog.com 
Jakob Nielsen's site www.useit.com
The Visual Display Of Quantitative Information [ISBN 096139210X], Edward Tufte
Envisioning Information [ISBN 0961392118], Edward Tufte
Visual Explanations [ISBN 0961392126], Edward Tufte
User Interface is easy to do badly, hard to do well, extremely rewarding and gratifying when done right.
Wiki Pages About User Interface
The term User Interface Contains some fairly deepseated and not too healthy assumptions about the state of the world, I personally prefer the term Human Interface. User Interface carries with it all the cultural baggage the term user (occasionally: luser) has in the world of programmers and engineers. The contempt and arrogance of this attitude is counterproductive and has produced more bad side effects than any other widely held bias in the Information Systems Professions, it is good practice to as much as possible expand the term user to be People Using The System. -- Larry Price
"User", perhaps, but "luser" originates with MIT's Incompatible Timesharing System, wherein it was an abbreviation for "Logged-in User". Although even there the pun on "loser" was irresistible, still, this was an OS where the login shell was a debugger; there were no idiot users, everyone was a programmer. So the jokes punning on "loser" had a very different weight than modern jokes about users such as the classic Problem Exists Between Keyboard And Chair. -- dm
I'm wondering if we could use a Category Usability or some such to collect some of the issues here, and refer to contributors to them: Donald Norman, Jakob Nielsen, and Stewart Brand (for How Buildings Learn). Certainly, Christopher Alexander cares a lot about usability.
Or is 'usability' too amorphous as a category? -- Jeffrey Miller
"usability" is not too amorphous, but it is perhaps too narrow. The wider terms are Human Factors or ergonomics (semi-pseudonymous), or Computer Human Interfaces (CHI) for Human Factors specific to computers (some chairs are ergonomic).
A list of general-purpose human-computer User Interfaces and projects thereof.
Complete interfaces:
Command Line Interface (Classic Unix)
The Humane Environment (Jef Raskin)
Individual features:
See original on c2.com