There's a lot of confusing regarding graphics cards today, and how it compares with just basic or integrated graphics as it pertains to the design business, so let me go through some comparisons and information as it might affect you.
First off, the latest integrated graphics engines out there (such as the Intel HD included with several of the latest generation of Intel processors, or the AMD Radeon 4250 found on the 880G chipset) are many times more powerful than integrated graphics a few years back. Graphical hardware performance has been probably the fastest developing and improving technology in the last ten years. This means that even integrated graphics (on newer platforms) offer high resolutions for large screen displays, as well as high quality color and display options. If you are wanting to do a lot of games on it, you'd need a dedicated graphics card, but again that's not pertinent to design use, is it?
So, why get a dedicated graphics card? Well, the general thought is, "A dedicated graphics card has its own RAM so it will free up space in your actual RAM." However, as I explained recently in another thread here, that's not exactly the case usually. Generally speaking, the computer must still set aside some RAM space even with a dedicated graphics card. This is because some of the data that is stored within the graphics card memory must also be stored within RAM if the CPU is to have access to calculate the data as well, as until recently there was no way for the CPU to directly access the memory on the graphics card.
In fact, it used to be that you considered a graphics card more powerful if it had more onboard memory (512 MB vs. 1 GB) however this simply isn't the case anymore. The days of making a card more powerful by slapping on more memory just doesn't work anymore. Most graphics cards today have 1 GB or so of RAM, and instead of adding more they make it faster and more efficient. There are a lot of other key factors that make graphics cards powerful. Just for example, the graphics card I previously had been running in my home computer was a GeForce GTX 280 with 1 GB of memory. The newer GeForce GTX 460 with only 768 MB of memory operates up to 20% faster than my GTX 280 even though it has less onboard memory AND half the memory bandwidth.
So again, why get a dedicated graphics card? That's getting harder and harder to really justify as integrated graphics are becoming so powerful today offering the features for designing that the dedicated cards offer, they just can't really support the heavily GPU oriented tasks like running demanding video games. However, there are some things that your system can benefit from for having a dedicated graphics card. First, a more powerful graphics card is going to be able to handle the programs and objects running within your operating system with more ease. For example, on an integrated graphics running at full 1920 X 1200 resolution, if you've got Firefox open playing a video as well as Adobe Photoshop rendering a workspace, there's sooo many pixels being output and rendered that when you start dragging around your Firefox and Adobe windows it may cause the video to freeze up, or windows to become a little unresponsive as you drag objects across the screen from one area of Adobe to the next. On a dedicated graphics card, though, it can use its more powerful GPU and the onboard cache to process this kind of work more fluidly than an integrated option.
Having a dedicated graphics card is going to also handle some of the work that is being done at the CPU level, meaning you'll have more system resources at the CPU free to do work. This is becoming less and less noticeable, though, as processors today have so much power and often so many cores!
Additionally, there's some software out there starting to take advantage of the incredible power in modern GPUs to help speed along calculations. The newer versions of Adobe software are just one example where, if you have a new graphics card capable of GPU acceleration, the software can use the power of the GPU to speed up renders and other very high-calculation tasks tremendously and does make a big difference.
If you do a lot of design work within Adobe using a lot of filters, layers, effects, etc. or you use any kind of software that deals with 3-dimensional design (such as a CAD software) then a dedicated graphics card is much more highly recommended. But, for your standard 2-dimensional graphics design, you're not going to be getting better color or image quality really - that's more dependent upon your monitor and color calibrations - or higher resolution outputs - most modern integrated graphics can handle up to 1920 X 1200 resolutions just fine for design type tasks.
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