Take for example the polynomial $p(x) = (x-3)^3$. If we expand the polynomial we would get $p(x) = x^3 - 9x^2 + 27x - 27$.
If we plug in $x = 0$ we get $p(0) = (0-3)^3 = -27$, which is exactly the value of the constant term of the polynomial. It makes sense we get exactly this, since every term except this one has an $x$. (Note we did not need to expand the polynomial to find this value.)
If our goal was to get instead the sum of all coefficients, that is, $1 - 9 + 27 - 27 = -8$, what value of $x$ should we plug in?