TN panels
Most flat panel monitors are TN (Twisted Nematic) technology.
These are popular due to their low cost.
TN panels have relatively poor viewing angles although they have been recently improved upon using 'TN+film' technology, where a layer of special film is added.
Vertical viewing angles are especially bad. Looking at even a modern TN panel from above or below can result in colour shifts.
Many TN panels use 18-bit colour and deliver less accurate colours making them not ideal for applications such as photo editing.

IPS panels
The most expensive panels are currently based on IPS (In-plane switching) technology.
They can achieve very wide viewing angles and excellent colour rendition. More recent S-IPS (Super IPS) panels achieve similar quality but at a much reduced cost.
For critical colour-based work, IPS panels offer the best quality but they are not without disadvantages. Their internal design means slightly less of the viewable area is given over to actually producing light, sometimes resulting in reduced brightness. Black levels can also suffer a little when viewed at wider angles.

The monitor needs to be calibrated to ensure that it is showing you an acurate version of your image.
Hardware can be purchased to achieve this. A number of companies make monitor calibration equipment.

Avoid any monitor with a glossy reflective screen as you will see as much of your own reflection as you will the image, and they are virtually impossible to calibrate for print output. This rules out Apple iMacs and Apple Screens.