A batter receives a reached on error when he reaches base because of a defensive error -- meaning he wouldn't have otherwise reached.
Reaching base on an error does not count as a hit, nor does it count as a time on base for purposes of on-base percentage. But there is still significant debate as to whether ROEs are undervalued in the statistical world, as certain players have a tendency to reach base via error more than others.
By definition, errors are primarily the result of a fielder making a mistake. But even with that caveat, certain players -- namely speedy ground-ball hitters -- are likely to record more times reached on error than the average player.
Watch: Jacoby Ellsbury reaches on an error.