The term 'Rule of Threes' usually pops up in reference to comedy writing, but it's also common in other forms.
When used in a list, the third point will be the punchline.
Example: The perfect pet are dogs, cats and salamanders.
That's clearly not a top joke, but you can see how the first two throw you off, then POW! Mexican walking fish!
In a longer form, in comedy, think of the race jokes. There's an Australian, a Frenchman and an Irishman. Whatever happens in that joke, the punchline will always be regarding the Irishman.
The story of the Three Little Pigs isn't a comedy, but the third is the punchline, in a way.
When writing ANYTHING, try to draw on the Rule of Threes.
Let's say you're writing a commercial and you have two scenarios, try to add a third. If you're left with four, cut the weaker to make three.
If I ever have to list items, I will generally list three specifics followed by something to imply there are many more options.
Example: You might choose to build your house with straw, sticks, bricks or another type of material.
That's only the tip of the iceberg but hopefully gives you a good understanding of the term.
See more of what I'm about here.