llavar is the infinitive of "to take".
llavarse is the reflexive infinitive of "to take for oneself".
The first thing you do is to drop the se at the end of llavarse leaving llavar. This is then conjugated to reflect the subject which is this case is "el". This leaves you with "lleva", however in doing this you now need to use the correct reflexive pronoun in front of lleva which is "se". this tells you that something is being taken by someone for himself or herself.Translated this will now say "he takes the food for himself." Now for further clarification you can add who takes the food for himself, in this case it is El monje.
So, now the translation is "The monk is taking the food for himself.
I think you may being getting confused with the se before the llava and the se after the llaver. Se tagged on the end of a verb simply means that it is reflexive. The se that you use in front of the verb is just one of the various subject pronouns used with reflexive verbs, ie me, se, etc depending on who the verb is reflecting upon.
I hope I haven't confused you further.