refers to the hallowed “Chamber of Records” in Khazad-dûm. It was here that the Dwarves kept their most treasured histories and documents. It was also the place where Balin set up his throne room, where he was buried, and the last survivors of his expedition to Moria died.
  In his notes, Tolkien offers the following explanation:

Mazarbul: chamber of.  √ZRB, probably "write, inscribe": mazarb appears to mean "written documents, records"; -ul as above?

We then have the root Z-R-B "to write, inscribe".  It may also include the idea of "recording, creating a written record".  It seems pretty much synonomous with the Arabic root K-T-B "to write".  From here, Z-R-B is placed in the same singular template as bark "axe", yielding zarb.  It's not certain if this means anything by itself.  The prefix ma- is added, which seems to indicate a past participle, and gives us mazarb "the written, inscribed".  Like Arabic, this passive participle is probably adjectival in nature, but can be used substantively (as a noun).  Arabic participles that are often used in this manner can end up being further lexicalized.  I can see this being the case here, so "the written, inscribed" can be interpreted as "a (thing) recorded", which is "a record".

Or, should that be "records", since the name in English is the "Chamber of Records"?  Zarb matches the template of bark "axe", so it would seem to be singular.  Arabic participles have plural forms, so perhaps the plural here would be mazarub, parallel to baruk "axes".  If mazarub is the plural "records", then why do we see the form Mazarbul instead of a construct phrase similar to Gund Mazarub?  Going back to the nature of participles in Arabic, they are primarily adjectival.  Because of that, a phrase like Gund Mazarub could be interpreted as "the hall/chamber that is being recorded".  It may even be ungrammatical since gund or "chamber" would be singular and Khuzdul adjectives should agree in number with the noun they modify, at least if they follow the pattern of Semitic languages.

Enter the suffix -ul here.  In the quote above, when Tolkien says "-ul as above?" he is referring to -ul in Fundinul.  There, he writes "-ul is apparently an adj. or genitive ending".  Calling it adjectival seems to be an accurate statement, as I have described in Duban Azanulbizar and Fundinul by comparing -ul to the Arabic "nisba".  This makes the word take on the meaning "related to the root noun", and so it then describes the chamber/hall/room as being related to things that are recorded.  It's not a chamber that is owned by records, or one that is found in and described by records, or that constructed of records (obviously absurd), or one that is for the activity of recording.  Instead, it is a chamber that is related to records, characterized by their presence, and therefore simply contains them.  Because of the use of the adjectival -ul suffix, it makes use of a plural form unnecessary. 

Because Tolkien wrote in the quote above that "mazarb appears to mean 'written documents, records' ", I think that's probably just a result of the English translation being "Chamber of Records" since we wouldn't say something like "the Recordish Chamber".

That same adjectival suffix seems to suggest that the word Mazarbul doesn't always appear alone.  Tolkien's notes don't indicate anything about the word "chamber" in the word Mazarbul.  Attempts have been made in the past to insert "chamber" into the gloss by pointing out that words starting with an m- prefix in Hebrew and Arabic are sometimes "nouns of place".   For instance, from K-T-B "to write" we get Arabic maktab "desk", or "a place for writing".  Again, though, Tolkien doesn't include it in his explanation, and it seems likely that it mirrors the name Duban Azanulbizar in that the first word, duban "valley" in that case, can just be left off and understood from context.  The word for "chamber" here is probably also not included.

The Lord of the Rings, The Fellowship of the Ring, Book II, ch 5
The Return of the Shadow, pg 467
The Treason of Isengard, 191
Parma Eldalamberon XVII: Words, Phrases and Passages, pg 47
The Letters of J.R.R. Tolkien, pg 186