Let $k$ be a field, and let $K_0(V_k)$ be the Grothendieck ring of $k$-varieties. One type of relation which defines $K_0(V_k)$ is the following: if $A$ is a $k$-variety and $C$ a closed subset of $A$, then $$ [A] = [A \setminus C] + [C]. $$ (Here, $[B]$ denotes the class of $B$ in $K_0(V_k)$.)
It is well known that $K_0(V_k)$ is a toy model for understanding certain (nonabelian) aspects of motives.
My question: why relations of type $ [A] = [A \setminus C] + [C]$ ? What is the connection with the theory of motives ?