"Tuhur" is purification or Wudu', while "Tahur" is water or something which is used for purification. According to some scholars, "Faith" means Salat. This is also the sense in which it has been used in the Qur'an: "And Allah would never make your Faith to be lost (i.e., your prayers)." [2:143]. Thus when Salat is the Faith, the purification is a prerequisite for Salat. Salat is not valid without purification. Some scholars are of the opinion that Faith here means Faith in general, as the Shari`ah defines it: To sincerely accept and believe in all that the Prophet (PBUH) came with, i.e., sincere acceptance of Allah and His Prophet (PBUH).
"Purification is half of the Faith" means the acceptance that purification is the most important article of Faith. It is like the saying of the Prophet (PBUH) that "Hajj is `Arafah", which means that `Arafat (the place where the pilgrims stay on the 9th day of Dhul-Hijjah) is the most important element of the Hajj. Thus, this Hadith stresses the importance and merits of purification and offers an inducement for it. It also mentions the eminence of the invocations mentioned in the Hadith by saying that if they are given a form, they will fill the space between the heavens and the earth. In other words, it is a description of the infinite vastness of the Mercy and Grace of Allah.