Language provides us with the framework with which we express ideas. Numbers, arithmetic, and calculus are the language of mathematics. C, C++, and Java are languages for computer programming. This is only partly true, as Guy Steele Jr. explains in Growing a Language. This perspective on language design extends far beyond programming.
I will focus on software related language design. It is an exercise for the reader to extrapolate how the same principles apply to literature, music, and other forms of human expression.
Just as Java is the most basic vocabulary and grammar with which more expressive languages can be designed, English is similar. The language required to produce a book is far more advanced than English vocabulary and grammar. Literary devices, plot structure, and character development are patterns that are designed into the language of literature. Similarly, design patterns make Java a useful language for programming.
The language of object-oriented analysis and design (OOAD) is the Unified Modeling Language (UML). However, UML is not very expressive by itself. It was not designed to be as precise as programming languages, because it was motivated by the needs of conceptual modeling. They thought that conceptual modeling is not precise. That is the tragedy of imprecise thinkers.
Now, they have caught on to the idea of using models to generate code. This requires precision; a machine only understands 1 and 0. There is no room for ambiguity. It is now a huge challenge to apply UML to this model-driven architecture (MDA).
We are constantly grasping for ways to improve how we express ideas. A thousand words are better expressed with a picture. The concepts represented by the geometric shapes are better expressed with tags. Patterns are recognized as we organize those concepts into more advanced ones. As a consequence, many thousands of instructions are captured in a blueprint with a small number of symbols. At each step, we seek to be more expressive with compact representations. This is language design.