Since you defined your question more clearly in the comments as relating to visual design, let me approach my answer from that perspective.
Visual design as I tend to define it relates to how graphic design principles are used in interface design to support clarity, consistency, and simplicity in order to create UIs that are easy and enjoyable to use. Wikipedia defines it as "Visual Design is a design working in any media or support of visual communication", which is a broader definition but still what I'm talking about.
The Visual Display of Quantitative Information by Edward Tufte is the single most influential book on visual design. Not only does it craft a compelling narrative for "visual design" as a separate profession, it gives you a ton of thinking about UI design and names patterns, such as the Least Effective Difference.
Some basic aspects of visual design that I think are important:
Every design decision is in support of the medium. What that means is that if you're doing visual design work for a web app, each choice you make should be relative to the fact that you're working on a web app which will be used by someone to achieve some goal. As such you have different priorities than graphic designers sometimes do and should make decisions accordingly. For instance, a common difference of opinion between some graphic designers and UI designers that I've seen has been whether or not to style input fields. Graphic designers may be looking for visual consistency as it relates to a theme or brand, whereas the visual designer in charge of the UI may be looking to create an easy to use and understand interface. Sometimes these goals clash, creating interesting conversations.
Typography. Large parts of interfaces are made up of text and as such you should grasp how typography can be used to affect how people use them. What are the consequences of Verdana vs Arial? Why do you want to stay away from serif fonts for screen-based UIs? Which fonts work well on mobile/small screens? Similar questions are relevant and, like above, a visual designer may make different choices than a graphic designer.
Contrast and colour. Both of these are designers' tools. Where a graphic designer may be interested in achieving a certain mood or atmosphere, a visual designer may prioritise contrasts and colours in a way that allows users to focus on essential parts of the user interface. Knowing your way around contrast helps you create legible user interfaces; colour is an essential tool for highlighting things, fading things out, and creating a consistent balance that delivers ease of use but doesn't conflict with any house styles or branding guidelines.
Whitespace and proportions. UIs are subject to the laws of proportions and composition like any other creative medium. Whitespace is a great way to draw attention to something without having to use superfluous colours, icons, etc. Know when whitespace works and how much you should use. Some designers cram everything together, making it hard to find things on the page, whereas some use too much (sometimes because they have 23" screens and don't notice). Don't be like them!
Iconography. Understanding how and when to use icons and having a basic grasp of how to create them goes a long way. Even if you're not a hot shot icon designer you should still be able to put together basic icons that communicate concepts effectively, and you should certainly learn how to distill ideas down into icon format because it's just useful to know how to do that. Ultimately though you'll likely want to work together with the graphic designer to figure out the best visual representation of business logic stuff and have her actually do the hardcore, detailed work on them.
Ultimately, if you're looking to improve your visual design skills, my advice would be to practice a lot.
I learned a lot from watching others, notably 37signals' designers Jason Fried and Ryan Singer, as well as keeping my eyes on trendsetting visual design like Quora, the team responsible for Facebook's visual design, Twitter, Google's UX team, etc. But that's me - I focus on web applications and minimalism. You may have different priorities.
In any case, always be on the lookout for interesting visual design by keeping your eyes open. Start following people on Twitter, subscribing to RSS feeds, and delving into books. And - of course - start designing your own stuff. There's no better way to learn than by doing.