Contrast Ratio: Contrast ratio represents the difference between the blackest black and the whitest white displayed on the screen. This sounds great, on the surface, but don't be wooed by an LCD boasting some ridiculous number here, like 40,000:1. The methods used to measure CR are dubious at best, with manufacturers coming up with processes to inflate the numbers, but never being able to reproduce those numbers with "real" images. That is why an LCD with 1000:1 CR and one with 40000:1 CR will receive the same comments on image quality: the testing is where the difference is made.
Aspect Ratio: Aspect ratio is simply the width to height ratio. 4:3 was once considered the "standard", what most of us are used to, but widescreen format and other variations are quite common. It is interesting to note, though, that standard sized monitors end up offering greater viewing area than their widescreen counterparts, even if they both have the same "inch" designation (ie: 17'' or 17'' wide).
Brightness: The brightness designation is given in cd/m² (candelas per square meter), and simply expresses how much light the screen produces. 200-300 is a good amount for standard computer tasks, like browsing and office productivity, but as much as 500 is recommended for gaming and watching movies.
Resolution: The most common maximum and recommended resolutions for monitors are 1280x1024 and 1680x1050 (wide). There are higher resolutions available, but upping the resolution ups the cost considerably. Are higher resolutions better? Not necessarily. Someone accustomed to 1280x1024 (not a shabby resolution in itself) would likely find a screen with a resolution of 1600x1200 to be a little difficult to see. Additionally, you need to make sure that your video adapter (be it a video card or on the motherboard) can support the screen's recommended resolution. Modern computers can handle 1280x1024, but older ones may need a lower resolution.
Pixel Response Rate: Pixel response rate defines the speed at which a pixel on the screen can change colors, and is given in milliseconds (ms). Some of the more common numbers you see in this role are 12, 8, 5, and 2. When we're talking about thousandths of a second, does the difference between these really matter? Only in some circumstances. A person who uses their computer for regular productivity tasks, and even movie watching will never see the difference between 12 and 5, but a person who is very into gaming and plays games where images on the screen change rapidly (especially common in First-person shooters) will notice the difference. The higher the number, the more chance that the user will experience "ghosting" in these situations. If you won't find yourself playing a lot of shooters like this then don't let the pixel response rate figure into your decision.
Viewing Angle: Images and colors on an LCD can distort and shift if you are viewing the screen at an angle, rather than facing it straight on. If you've had any experience with LCDs at all you more than likely have already noted this. Viewing angle defines the angle that you can view the screen without experiencing any distortion. If you're only ever going to be looking at the screen straight on, then don't worry about this spec. If you think it will figure in, then go to a store and test out screens with different viewing angles to see what you need.