This is due to Fermat's principle, which states that light travels between two points along the path that requires the least time, as compared to other nearby paths. Light travels more slowly in a denser medium, and hence will bend more toward the normal.
Why then does light follow this path, and not other paths? This is because light also obeys the principle of least action, and the action for light is proportional to the distancetime for which it travels. Thus, least action requires least distancethat the time taken be minimal.