Hi Katerina. That is the literal translation of it. PS I am using an older computer which doesn't always register other peoples answers so apologies to them if they have already given the same answer.

Cleanliness is part of belief

I think you are more curious about the meaning of it than the closest natural equivalence word to it in English.

You could not find it in the Qur'an explisitly. The sentence come from His Apostle (Muhammad SAW).

Actually the sentence has implisit meaning.

For the explisit meaning; Could you imagine moslem must take a bath (wash their face and limb with water) and was suggested to brush their teeth before pray five time a day. Moslem must clean before open connection with Allah in official way.

For the implisit meaning; Moslem must clean their belief/faith from anything beside Allah (God & His embodiment),

Read Sura at-Taubah:

Say: "If it be that your fathers, your son, your brother, your mate, or your kindred: the wealth that you have gained; the commerce in which you fear a decline; or dwelling in which you delight are dearer to you than God, and His Apostle, or the striving in His Cause, then wait until God Brings about His decision: and God guides not the rebellious." (IX:24).

God (God & His embodiment)
Islam requires of us to believe in God and his Apostle, and observe Namaz (shalat), Roza (puasa), Zakat dan Haj (Naik Haji), and lead a life of piety and honesty and goodness and gentility and moral and social rectitude and self-discipline.

(Note: the God in Islam not a man or woman, Allah has substantially different substance :)).

I hope it has a little contribution to address your curiousity