|If the video card has better specs than the onboard video then, yes.|
The picture quality depends on the resolution--the number of pixels displayed on the screen--and the number of colors available for each pixel. Think of each pixel as a little box on the screen. For an 800 x 600 resolution you have 480,000 boxes. For a 1024 x 768 resolution you have 786,432 boxes. The more boxes you have the smaller they must be to fit the screen so higher resolution gives you a clearer picture.
The number of colors is a binary thing. 2^8 is 256 so 8 bit is 256 colors. 2^16 is 16 bit color and gives 65,536 colors and so on.
The maximum resolution and number of colors depends on how much video ram you have so generally the more ram a card has the better the picture will be.
Other video card specs are the refresh rate or horizontal frequency, which is a measure of the number of times per second the screen refreshes itself and gigaflops or gflops which is a measure of the computing power of the video processor. Those affect video more so than a still picture.
Some practical considerations are that if you're viewing a digital picture from a file, that picture already has preset resolution and colors so you won't get more detail by viewing it on a monitor set at higher values. The picture information is coming from the file and not the video adapter. Another consideration is that as you increase the resolution and colors you reach a point where your eyes can't tell the difference. So it may be hard to tell the difference between high resolution and very high resolution (however those arbitrary specifications are defined). Third, your monitor has to be able to display the picture the video adapter sends to it. For example, an older monitor may not be able to display a resolution above 1024 x 768.