In general in play they were ignored or just treated as an abstract language with no further comment.
As to where they came from, here's an answer from Gary Gygax on Dragonsfoot!
As D&D was being quantified and qualified by the publication of the supplemental rules booklets. I decided that Thieves' cant should not be the only secret language. Thus alignment languages come into play, the rational [sic] being they were akin to Hebrew for Jewish and Latin for Roman Catholic persons.
I have since regretted the addition, as the non-cleric user would have only a limited vocabulary, and little cound [sic] be conveyed or understoon [sic] by the use of an alignment language between non-clerical users.
If the DMs would have restricted the use of alignment languages--done mainly because I insisted on that as I should have--then the concept is vaible [sic]. In my view the secret societies of alignment would be pantheonic, known to the clerics of that belief system and special orders of laity only. The ordinary faithful would know only a few words, more or less for recognition.
In other words, it was supposed to be more like religious languages, but wasn't really well thought through. It disappeared in Second Edition and was not missed.
Languages don't come from stats, ability scores, or skills. They come from race, and possibly from class or background.
Languages
By virtue of your race, your character can speak, read, and write certain languages. (PHB p.17)
From their first mention languages are set out as a racial benefit. Two exceptions arise--Druidic and Thieves' Cant--as class benefits. Later, we see that knowledge of a language may arise from a background (p.125) or from extensive training (p.187). Which gets us to my interpretation:
Languages are part of your deep background.
Language acquisition as a racial feature arises from assumptions about segregated communities; the DMG (pp.20-21) discusses ways in which one might adjust these assumptions and how that might impact language acquisition. (They give the example of a racially-blind kingdom-dependent language system as an alternative.)
Language acquisition as a class or background feature is more-explicitly based on long times spent in the relevant community/diverse settings/life of study. Note the acolyte and sage gain two languages; guild artisan, hermit, noble, outlander each gain one. Alternately, you can pay to train for 250 days and 250 GP. This also constitutes a large amount of time, effort, and investment on the part of the character.
Thus, changing your ability scores, statistics, or skills have no effect on your languages. Because those changes haven't changed your experience, by which you acquired language. (Admittedly, those changes might impact your ability to hear, speak, read and/or write, however.)
Languages aren't a skill. They aren't tied to an ability modifier and your broficiency bonus in that way because they're binary: you can't (RAW) be more- or less-skilled in a language.
Languages aren't pegged to attributes. But they used to be. Originally PCs were guaranteed two languages: common and alignment. INT>10 made it possible to know more languages. In 1e your intelligence capped the number of languages beyond your base (racial/class) languages that you could know. In 2e your intelligence capped the total number of languages that you could know, all the way down to INT=1 capping you at zero languages: "while unable to speak a language, the character can still communicate by grunts and gestures." (PHB1e p.10, PHB2e p.16)
[ed.: I'm working off of retroclone material for the Original cite: if anyone's got a good cite to edit in I'd appreciate it.]
Is it related to personality? Personality isn't really a defined term in D&D, so this gets sticky, fast. For our intents I think it's easy enough to say "no," but recognize that language and personality formation are interwoven in real life in a way our game just isn't trying to simulate.
Best Answer
Maybe Dwarvish or Draconic
I had a search through resources for 5e and previous editions, but couldn't find mention of the script used for the Aarakocran language. In fact, Aarakocra doesn't seem to have existed as a language in its own right before the publishing of the EEPC; according to their original entry in the 5e Monster Manual, they only speak Auran, with no mention of a native language of their own. In 3.5e they are noted as speaking Common and Auran.
Aarakocra seem to be generally described as being dwellers of the Elemental Plane of Air (where you'd expect Auran to be the primary language) and are all fluent in Auran already. It seems plausible that the Aarakocra language is derived from Auran - and Auran (in 5e, at least) is itself a dialect of Primordial, which the PHB states uses the Dwarven script, so maybe Aarakocra does too.
Alternatively, in prior editions the different elemental languages were not so related to each other, and they used different scripts. 3.5e describes Auran as using the Draconic alphabet, so that could also make sense (maybe the draconic script is easiest to write using talons).