A constitutive equation is like a recipe that tells you how to turn one thing into another thing. Just like if you follow a recipe to make cookies, you add flour, sugar, eggs, and other things to make the dough.
In science and engineering, people use constitutive equations to figure out how materials will behave under different conditions. So, for example, if you wanted to know what would happen to a rubber band if you stretched it really far, you could use a constitutive equation to figure it out.
The constitutive equation would say what the rubber band is made of (rubber), and how it will change when you stretch it (it gets longer and thinner). It might also tell you how much force it can withstand before it breaks.
Basically, a constitutive equation is just a rule that helps scientists and engineers understand how things behave and how they can be used.