Normalized histogram is on the same scale as density, and this is convenient if you want to compare empirical histograms with some theoretically obtained density (i.e. to superpose them on the same graph), or compare two histograms with differently selected bins.
Added: We can view each bar in the normalized histogram as an estimate
of the value of probability density function at some nearby point
(provided that density doesn't change much along the width of each bin).
If two histograms come from the same distribution, both should resemble
the same density function --- up to uncertainty introduced by sampling.
Without normalization, the height of each bar would also depend on the
sample size and the width of each bin.
Note that there are, also, other ways to visually compare empirical
distributions of two random samples, for example Q-Q plots.