A walk-off hit is a hit that ends the game (and allows everybody to walk off the field). Thus it is a hit that scores the winning run for the home team in the bottom of the ninth, or in the bottom of an extra inning.
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A walk-off hit is any hit that drives in the winning run of the game. The more common variation of this would be a "walk-off homerun," or a homerun that ends the game as a win for the batting team.