The Mishna Berura (O.H. 158:1) explains that Netilat Yadaim was enacted for two main reasons. The first is that the Kohanim were Rabbinically obligated to wash their hands before partaking of Teruma (a type of priestly gift) since the laws of ritual purity and impurity were in effect when the Bet HaMkidash stood. This Sages therefore extended this requirement to wash to any Jew who wishes to eat bread so that everyone could be accustomed to eating in ritual purity. The Levush (ibid.) explains that one is required to wash one’s hands specifically for bread because the main component of Teruma was grain-based.
The second reason for Netilat Yadaim is based on the verse “You shall sanctify yourselves and be holy” (Vayikra 20:7), which teaches that one should be accustomed to eating in a spirit of cleanliness and holiness. The Shulhan Aruch (Orah Haim 158:1) codifies the law of Netilat Yadaim and mentions that it should be done regardless of the ritual status of one’s hands.
The Shulhan Aruch (Orah Haim 158:9) explains that one who is flippant aboutNetilat Yadaim is liable to banishment from the community, is at risk of poverty and, because one is not heeding our Sages’ enactments, is taken prematurely from this world. Even practically speaking, Netilat Yadaim is likely responsible for having prevented countless plagues over the centuries which were transmitted on people’s hands.
Summary: One should wash Netilat Yadaim with a sense of reverence.