The only thing Tolkien tells about aglâb is that it is equivalent to the Elvish lambe, which is a "spoken language" or "tongue". It doesn't mean "language" in general; rather, it is a specific language. So, Khuzdul is an aglâb / lambe, Sindarin is an aglâb / lambe, Quenya is an aglâb / lambe, etc. Tolkien also says that it might be better to translate as "dialect".
The Elvish word lambe is related to their words for "tongue", which is why lambe refers to a spoken language. However, that's probably not the case for aglâb. The reason is that it apparently shares the radicals '-G-L with iglishmêk, which according to Tolkien is a "gesture language". We could think of it as sign-language", perhaps similar to the signs used to communicate by baseball teams, or maybe even as developed as American Sign Language. Iglishmêk probably has nothing to do with the physical tongue, and so we need to look elsewhere to find a possible meaning for the radicals '-G-L.
The best explanation I have found is that '-G-L is related to "speaking". Arabic has a number of roots related to "speech" which may include words for "to speak", "word", "utterance", "phrase", "language", etc. The root that seems most similar to aglâb and iglishmêk is L-Gh-W, from which the words laghâ "to speak" and lughât "word" are created. It's interesting to note that the sounds used in the Arabic root L-Gh-W is similar to the (hypothetical) Khuzdul root '-G-L. This circumstantial evidence may lend some extra weight to the idea.
In Arabic, the suffix -at has been used to form the feminine gender of nouns and also abstract or collective meanings. This may be why the suffix also shows up in some Arabic plural patterns. The collective derivation should not be confused with the collective number. Instead, it forms a new word from a grouping of the stem word. This may be the case with -âb in Khuzdul. If there is a hypothetical word agal or âgal that means "word, utterance, or phrase", the composition form would be agal. When the suffix -âb is added, the second /a/ is dropped due to being unstressed. A collection of words, utterances, or phrases could very well be taken to mean a "spoken language". It's possible that there is a singular form ugl "word, utterance, or phrase", and the plural form is agâl. The composition form would again be agal, to which to the suffix -âb would be added.
Aglâb is then "language, tongue, dialect" and is singular, nominative, composition.
The War of the Jewels, pg 395