Let $k = \mathbb C$. Given a commutative $k$-algebra $A$, an $A$-module $M$ and a homomorphism of $A$-modules $s:M \to A$, we can construct the Koszul dg algebra. $$K(A,M,s) = \wedge^{-\!*}_A(M)$$ (Here the complex concentrate in nonpositive degrees.)
According to Toen, given a vector bundle $V$ over $X (:=\mathrm{Spec}A)$ and a section $s:X \to V$, we can construct a Koszul complex $K(A,M,s)$, where $M=\Gamma(X,V)$. But the section does not seem to give any homomorphism $s:M \to A$ unless we choose a metric on $V$.
Question: how can we naturally define a homomorphism $\Gamma(X,V) \to A$ from a sction of $V$?
$\DeclareMathOperator{\Spec}{Spec}$$\DeclareMathOperator{\Hom}{Hom}$$\DeclareMathOperator{\Sym}{Sym}$Looking through your source, this seems to be the setup: Let $A$ be a ring, $X = \Spec(A)$, $M$ an $A$-module. Then $\Sym_A(M)$ is a (commutative) $A$-algebra, and set $V = \Spec(\Sym_A(M))$, which is a scheme over $X$, i.e. has a structure map $\pi : V \to X$ (induced by the ring map $A \to \Sym_A(M)$).
Now giving an $A$-module map $M \to A$ is equivalent to giving an $A$-algebra map $\Sym_A(M) \to A$, by universal property of $\Sym$. But this in turn is equivalent to giving a morphism of schemes over $X$ from $\Spec(A) \to \Spec(\Sym_A(M))$, i.e. a section $X \to V$. Thus sections $s : X \to V$ are equivalent to $A$-module maps $M \to A$.