What does simplicity mean?
In Oxford Dictionary, simplicity means the quality or condition of being easy to understand or do. Another words, to keep it simple means to emphasize the fundamental and straightforward nature of something.
Simple design does not necessarily means uncomplicated in form or color pallet. What it does mean - the feeling of no difficulty, when everything in space is easy to understand, when you have no questions, you don't need to wonder because all around you is easy and save.
There were humans long before there was design. And to understand the psychology of simple design we need to turn to the basic principles of human behavior.
Why there is a huge desire in us to understand everything? To understand means to be prepared and to feel safety. To understand the principle of design is to live peacefully in it.
To understand a complicated thing is easier through breaking it into simple pieces. That's why if you want to create a complicated form it's better to do it using simple forms (circle, square etc.). If your design space is really busy and compound - emphasize simple (fundamental) elements to give your mind a break - pave the way to understanding the complexity.
Simplicity in design does not mean white box, but safety and prediction.