From my experience design patterns are both taught and used as a starting place for solving a problem which is recognized as similar to a problem which was previously solved effectively with in the manner of the pattern. Rarely will the design pattern fit perfectly as the solution, but by recognizing and using the correct one as a starting point for many architecture related problems you can greatly reduce the work involved, in creating the solution.

They keep people from re-inventing nearly identical solutions over and over, and allow for a vocabulary which can express rather complex ideas because fellow practitioners of software engineering generally know many of the same design patterns. This saves time and reduces the opportunity for miscommunication when expressing a more complex idea (assuming the person you are talking to doesn't lie and for instance say they are familiar with the facade pattern, when they are not).

To me this is using them to both get and express a better understanding of a complex system. I am also able to understand code for new projects I am to work on much quicker when I understand the underlying design of the elements. When the elements are designed with a structure that resembles things I am familiar with this process becomes fairly easy.

I see them as things like definitions of 'Suspension Bridge', 'Victorian House', 'Tunnel', or 'Dog House'. Sure we might see a book consisting of very rudimentary definitions of structures like these as being absurd, for the corresponding type of engineer, but that is because of our familiarity with the form these structures take. That familiarity with the form is the point of design patterns in my opinion. And I believe their utility is indispensable should we want to continue building more complex structures in code.