We must ritually wash our hands before eating bread regardless of the state of their cleanliness or otherwise. As we noted in the previous shiur hygiene and cleanliness are but one of the reasons for performing netilat yadayyim. The considerations of ritual purity (as opposed to physical cleanliness) and sanctifying our mundane functions require netilat yadayyim even if our hands are physically clean.
The complete text of the benediction which we associate with washing the hands is as follows:
Barukh attah Adonai, Eloheynu melekh ha-olam, asher kiddeshanu bemitzvotav vetzivanu al netilat yadayyim.
A non-literal rendition of this benediction in English would be:
Praised be God, Sovereign of the Universe, whose commands sanctify us, one of which is the command to wash our hands.
The reason why I have chosen to offer a non-literal rendition in English is because the origin of the Hebrew phrase al netilat yadayyim is not clear. The root natal is borrowed from the Aramaic. In Aramaic the meaning is "to take". Thus it is quite possible that the original meaning was "to take water to the hands". Indeed, in many classical sources the action is actually referred to as notelim la-yadayyim - "taking [water] to (or for) the hands". Another suggestion that has been offered is that the verb derives from the Aramaic noun natla which denotes the utensil from which the water is poured. However, this order of derivation is highly unlikely: it is much more reasonable to assume that the natla received its name because it is a utensil used for netilat yadayyim rather than that the utensil named the action. A third suggestion, that the verb natal originally meant "pour" is even more obscure and is, as far as I can discover, unfounded.
The text of the benediction states that netilat yadayyim is a divine command. However, as we learned in the previous shiur, the requirement that we wash our hands before eating bread is, in fact, of rabbinic origin. It is one of seven mitzvot which ascribe to their action the force of Torah law but which are an innovation of the sages. (You will find all seven listed in Shabbat 016.) The rationale that the sages offered is that these commands are indeed of Torah origin: the source is to be found in Deuteronomy 17:11 -