"Three" little pigs, the "three" Muskateers, ever wondered why characters in our childhood stories, frequently came in set of three ?
The "rule of three" is a writing technique, that helps writers engage with its audience on a deep psychological level. A set of three digits, in specific, leaves a strange psychological impact on our brains that helps us remember things better. The next obvious question, would be, why not four or two, or any other number for that matter?
The "Three" Muskateer (Source)
Why three birds in hand are a better than a hundred others in the bush
This is because, as human beings, we are better at recognizing patterns and shapes and three is the minimum number that makes creating this shapes possible. It's neither too large, nor too small making it the perfect sweet spot.
The polygon with least number of sides is a triangle., which has three sides
Learning shapes comes easier than words, because our ancient forefathers were better at remembering visual cues more than raw data. We learn words through association, A list of three is highly cohesive as a memory device, despite being small in magnitude.
Another indicator of this gift of ours is that good IQ tests, assess pattern-based skillsets as a fair indicator of intelligence, as it requires little to no prior knowledge to answer them. This removes the element of rote learning, unfair unadvantage of having access to intellectual resources, making it more accurate than verbal or scientific reasoning. This indicates that we are wired to recognize patterns more efficiently than anything. The number three, even as a bulleted list or a simple sentence, subconsciously appears as a pattern enabling us to remember it better.
Now that we know the significance of three, we know the secret why Goldilocks, met a family of exactly three bears or why Julius Caesar bragged "Veni, vidi, vici" in his letter to the Roman Senate in 47 B.C.
The effective nature of the number three isn't just understood implicitly in the form of storytelling. The Latin phrase "omne trium perfectum" tells us that we knew it impact long ago, which translates to "Everything in three, is perfect."