Unilateral neglect is a phenomenon which may occur after damage (whether from stroke, trauma or other causes) to either hemisphere of the brain, although it is more common in right hemisphere damage. For the purposes of this writeup, right sided damage will be assumed.
Unilateral neglect (aka hemispatial neglect) is the failure to perceive stimuli coming from the left side. These stimuli may be auditory, visual, or tactile. In other words, the patient acts as if the left side of his world had ceased to exist. There is also the phenomenon of extinction, where if two stimuli are presented simultaneously, only one will be perceived (i.e. touching both hands at the same time, only the touch on the right will be felt). This phenomenon can be tested by, for example, asking the patient to draw a symmetrical object (clock, flower, face..), or to bisect a straight line. A patient with unilateral neglect will draw only the right half of the object, or will mark the line 3/4 of the way to the right (bisecting the 1/2 that he perceives).
As a consequence of this, the patient acts as if nothing to their left existed - they eat only the food on the right side of their plate, shave only the right side of their face, only see things to the right of them etc. This phenomenon may extend to the patient's own body. For example, patients with this problem have been found lying next to the bed on the floor, and when asked what happened, related that they awoke and there was a severed leg (or arm) in the bed with them, so they threw it out - and somehow got thrown out along with it! These patients are truly unable to perceive that the arm or leg is, in fact, attached to them and a part of their body.
This makes rehabilitation difficult - it is hard to work on deficits in a body part the patient does not acknowledge as their own. Sometimes patients can be taught to turn in a circle so that eventually the entire room goes through their right visual field, thus allowing them to see whatever they are looking for. This is one of the deficits that patients are truly completely unaware of.