Undoubtedly, Wudu possesses two manifest benefits - the medical benefit and the ethical and spiritual one.
From the medical point of view, washing of the face and hands five times a day or at the very least, three times a day, has an appreciable influence as far as the cleanliness of the body is concerned. Wiping the head and the exterior portion of the feet - the condition here being that the water reaches the hair and the skin -means that we keep these portions clean too.
We shall allude later when discussing the philosophy of ghusl, that the contact of water with skin has a special effect in achieving the equilibrium of the sympathetic and parasympathetic nerves of the body.
As for the ethical and spiritual aspect, since it is performed for Allah and with the intention of pleasing Him, it possesses an educative influence; especially since its implicit meaning - from head to toe I strive to obey You - serves to corroborate this ethical and spiritual philosophy.
In a tradition, Imam ’Ali b. Musa al-Ridha (a.s) says: “The reason why the order for (the performance of) Wudu has been issued, and (the reason) why the acts of worship should commence by it is that when the servants stand before Allah and converse with Him, they should be clean, away from uncleanness and pollution, and act in accordance with His orders. Apart from this, Wudu eliminates drowsiness and lethargy from man so that the heart can acquire the purity and luminosity for standing in the presence of Allah.”
When we explain the philosophy of ghusl, the philosophy of Wudu should become more clear.
Source:
180 Questions Enquiries About Islam
[Volume One: The Practical Laws, P: 17].
Ayatullah al-`Uzma al-Hajj ash-Shaykh Nasir Makarim Shirazi
The Islamic Education Board of the World Federation of Khoja Shia Ithna-Asheri Muslim Communities