Very roughly, the DT invariant is a generating function $\sum q^k e(M_k)$ of a numerical invariant $e(\cdot)$ of a sequence of moduli spaces $M_k$. The motivic DT invariant is obtained by considering $\sum q^k [M_k]$ where $[M_k]$ is the image in $K(Var)$. This contains more info than the ordinary DT invariant.