This form of meditation denotes "before the eyes," which refers to direct experiential perception.
Thus, the type of seeing denoted by "vipassanā" is that of direct perception, as opposed to knowledge derived from reasoning or argument.
Vipassana meditation consists of an energetic observation of physical objects, mental representations (nama and rupa) and thought-processes in their aspects of impermanence, unsatifactoriness and lack of an "inherent", independent essence or self.
To see through impermanence means to examine whether things are permanent (duh). To see through the mode of unsatisfactoriness means to examine things as to whether they are satisfactory or are "imbued with stress or suffering". To see through the mode of non-self means to examine things as to whether they have a permanent identity or self, or an essential nature.
In Vipassanā meditation, the meditation object is one's own consciousness, one's consciousness while observing, say, the breath (as in ānāpāna meditation).
In this context, the modes of seeing refers to focusing on those aspects of consciousness which appear to have (or not have) these characteristics.
Vipassanā is primarily a meditation on the physical sensations of the body. The meditator develops their goal through observing sensation without craving or aversion, thus developing an understanding of sensation's true nature.
Today, the term "Vipassanā" also refers to the meditation technique used by many branches of modern Buddhism called Theravada (practiced in modern Sri Lanka, Burma, Laos and Thailand).
This also referes to a specific branch of Buddhism popularized by an Indian businessman named S.N. Goenka and his mentor U Ba Khin as a nonsectarian form of Buddhism, and also by Americans Joseph Goldstein, Sharon Saltzberg and Jack Kornfield (who were inspired by the monks Mahasi Sayadaw and Ajahn Chah).
Vipassana is also practiced under the name "insight meditation."
Vipassana is just one meditation technique.