Adidas does not stand for anything; it is a name created as the result of a threatened lawsuit. The company was named Addas before it became Adidas.
It might seem at first glance as if the company's founder, Adi Dassler, had simply combined his first and last name and then dropped the last four letters, but that is not the case. The company was registered in June of 1948 as Addas, but another German company, Ada-Ada, was going to sue Addas because the names were too close. So, rather than create an entirely new company name, Dassler avoiding the lawsuit by adding the letter 'i' between the d's.