"Did so" means that that was the reason that they made that theory.
During the first half of the 20th century, linguists who theorized about the human ability to speak "did so" from the behaviourist perspective that prevailed at that time. They therefore held that language learning, like any other kind of learning, could be explained by a succession of trials, errors, and rewards for success. In other words, children learned their mother tongue by simple imitation, listening to and repeating what adults said.
What is the meaning of "did so" in this Paragraph?
Yes, "did so" refers back to the linguists action where they "theorized about the human ability to speak".