The pop-sci answer is that Lorenz characterised chaotic atmospheric dynamics with the hypothetical example of a butterfly's flapping wings changing whether a tornado results. However, since butterfly-shaped solutions in the Lorenz attractor are sometimes called Lorenz butterflies, my question is: was the butterfly effect named for the shape of the plot or the hypothetical scenario of a butterfly's effect?
SEE for more
Ed Lorenz in 1963 wrote
One meteorologist remarked that if the theory were correct, one flap of a sea gull's wings would be enough to alter the course of the weather forever. The controversy has not yet been settled, but the most recent evidence seems to favor the sea gulls.
Following suggestions from colleagues, in later speeches and papers Lorenz used the more poetic butterfly. According to Lorenz, when he failed to provide a title for a talk he was to present at the 139th meeting of the American Association for the Advancement of Science in 1972, Philip Merilees concocted Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas? as a title.
I believe both of these were earlier than the possibility of computer images of the Lorenz attractor.