Do the english user translate "monk making it his object to let go" as "monk knowing nibbāna", right? I ask this question because in pali, "to let go (nibbāna)", in this context, is known by monk. It is not just a target. The (ariya) monk thinking of nibbāna in his concentration, in this context.

I just wanna make sure that english translation is right, because when I translate that english sentence, by my terrible english, it look like "to let go " and "object" means "target", not "something is known by monk".

In the pāli: ārammaṇa means "something is known by consciousness", "something is thought by consciousness", "external sense-fields". It doesn't means target/object.


  "And what is the faculty of concentration? There is the case where a monk, a disciple of the noble ones, making it his object to let go, attains concentration, attains singleness of mind. 
  http://www.accesstoinsight.org/tipitaka/sn/sn48/sn48.010.than.html




Edited:

It should to be:


  "And what is the faculty of concentration? There is the case where a monk, a disciple of the noble ones, making "to let go" as his mind's focus, attains concentration, attains singleness of mind.
it look like "to let go " and "object" means "target", not "something is known by monk".

Yes, I think the English is a bit ambiguous, and it could be understood to mean either (or both).

The word "object" has many meanings, of which two are:


  
  a person or thing to which a specified action or feeling is directed.
  "disease became the object of investigation"
  synonyms: target, butt, focus, recipient, victim
  "he became the object of fierce criticism"  
  a goal or purpose.
  "the Institute was opened with the object of promoting scientific study"
  synonyms: purpose, objective, aim, goal, target, end, end in view, plan, object of the exercise
  


So an English reader might understand it as the focus of meditation (what you're attentive to), or as the purpose of meditation (what your aim or ambition is).