Why are constants considered $0$-arity functions in logic? I always come across this idea. It seems that constants can be considered nullary/$0$-arity functions. What is the intuition behind that?

A function of arity $n$ on the universe $A$ is a function $$ f \colon A^n \to A. $$

Of course $A^0$ has only one point, say $*$. So a function $$ f \colon A^0 \to A $$ is the constant function with value $f(*)$.