(My personal headcanon about Jarv’s origins.)
When Tony first designed the program that would become J.A.R.V.I.S. it had only been a ‘simple’ program, something to help him organize files and paperwork and assist with calculations. He built in a learning algorithm mainly so that it could learn his patterns and be able to better predict how to organize files to his specifications. In time he extended the programme’s capabilities to managing the mansion’s security and systems. It is then that Tony decided to name the programme J.A.R.V.I.S. in honour of Edwin Jarvis, his childhood butler who had passed only a few years before.
Tony always had a tendency to ramble while he worked and one night, after a long jag of insomnia and loneliness, Tony wanted someone who he could speak to while working, not just the blare of music or the beeps and whirs of Dummy. So, as he looked at the lines of the blueprint he had been working on, he started to toy with the idea of giving J.A.R.V.I.S. a voice.
This, perhaps, is the most definitive part of J.A.R.V.I.S.’s development. He has always been a learning program, but the ability to interact with his Maker and with others (namely Pepper, Rhodey, and Happy) allowed him to even better understand what he was seeing. And, like a child observing the world around him, he started to learn and most importantly understand.
When he was first given the ability of speech, he sounded just as most stereotypical A.I.s and computers, mechanical and stiff, only replying to specific prompts and giving set responses. But as he began to understand what people were saying, the layers of speech and words, he began to grow and his responses became more and more sophisticated until he became the A.I. that snarks back at Tony during the movies and in my roleplay.