The old CRT (Cathode Ray Tube) monitor is an analog device. That means that your graphics card must convert the computer’s digital signal into a signal that the CRT monitor can understand. Of course, there’s always something lost in the process.
The LCD monitor is a digital device. If you use the DVI connection there’ll be no loss of image quality or signal corruption. That is why you get a crisper image.
Here’s the snag: if your graphics card doesn’t have a DVI connector then you’re stuck using the old VGA connection. Your LCD monitor should have a VGA connector as well, but keep in mind that you’ll be getting an analog signal so it won’t be as clean as purely digital. It may be worth your while to get a new graphics card with either DVI-D (digital only) or DVI-I (digital or analog with adapter) connectors so you can get the most out of your LCD monitor.