>To get something fixed, it is required to make a noise to get attention
>The one who complains gets their issues fixed
>To get attention be loud and noticeable not quiet
The phrase originates with the invention of the car and it being something that was adopted quickly by every household in America. When people were new to having them though, it was only when a wheel would squeak that it would be greased since nobody was used to the servicing of cars as often, back then. It has since become a synonym for someone who complains to get the goodies and is a popular phrase in regular parlance all over the world.
Example
This lawyer is more successful probably because the squeaky wheel gets the grease
>In a competitive industry such as this one, you should know that only the squeaky wheel gets the grease