To me the most important specs (once you've decided on a size and resolution) are:
Contrast - Difference between black and white, which is important for all monitors
Response Time - Not to be confused with refresh rate (which is almost always 60Hz), response time is how long it takes an individual pixel to change from one color to another. If this is too slow, gaming and videos will "ghost" and look blurry. Not as important for photography and graphic design.
Color Space (Gamut) - Generally measured in percent of NTSC covered. A good monitor will have 90+ percent coverage, a great monitor will go over 100. This is less important for gaming (games aren't designed with a "wide" gamut in mind) but is critical for photography.
Sadly, there's often a tradeoff between the last two. TN-based models tend to have better motion, but they have worse color accuracy compared to an IPS-display.
There are other factors that are less directly related to the panel used, such as the coating on the screen. Also, Apple laptops tend to have some "baseline" calibration right out of the box, which can make the display more pleasing to look at.
If you're interested in the whole story, there's an extensive discussion on Anandtech