What is meant by the above hadith - "cleanliness is half of faith" is more than what could be gathered literally. The Ulama have interpreted many different meanings to this Hadith, and the most appropriate meaning is that the word "Imaan" in the Hadith refers to Solat as in the Qur'anic verse:
" وما كان الله ليضيع إيمانكم "
- and thus Wudhu is a condition for Solat, and so it is as if though it is half of Solat.
(Tuhfatul Ahwazi: Darul Hadith: Kaherah)