Constants make your code self-documenting. const int DAYS_IN_WEEK = 7; is clearer than using the number 7 directly in calculations. If you need to change a value used in many places, you only update the constant definition once.
Without constants, you have to find and change every occurrence of the value. Constants prevent accidental modifications. If you write PI = 3.14; later in your code, the compiler stops you instead of silently breaking your calculations.