In the temple this practice was part of a reenactment of the process of dedicating the Kohanim, imbuing them with their special status. The daily reenactment guided them to live every day as a fresh beginning and to raise their consciousness to who they are and what is their role.
The Bible describes the entire children of Israel as a nation of priests. Applying to all the practice of pouring water reflects this Biblical idea that we are all priests and that the world around is like the temple, an arena in which we are called forth to serve.
Another meaning of netilat yadayim emerges from the Kabbalah. The human realm parallels the divine and thus sanctifying the hands reflect the belief that human endeavor can be divine.