Browser-based games are games that require no downloading of an installer, or some stand-alone program that sits on your hard drive. They are games that are played from your browser without committing many resources to them. Most browser-based games are also text-based, featuring few if any graphics like Kingdom of Loathing or NationStates. Others, such as the popular RuneScape feature the opposite, and actually have more advanced graphics.
Most use plug-ins like Adobe Shockwave, Java or Adobe Flash.