Why are variables important in java?

Answer 1

We need to store data somewhere.

Answer 2

Java is an Object Oriented Programming (OOP) language. Therefore, Java depends on created objects in order to perform operations. Variables are objects. As a result, variables are the "back-bone" of OOP. As @Steppenwolf pointed out, variables store data and in order to perform more complex OOP operations like constructor overloading, mutations, etc. OOP requires variables, they are unavoidable.