defintion of weak solution

Question

i found that a weak solution of $-\Delta u=f $ where f $\in L^{2} (\Omega)$ is a solution u $\in H_{0}^{1}(\Omega)$ and it is solution in sense of distribution so what does it mean that that u is solution in sense of distribution? is that for every $\phi$ in D($\Omega)$ we have $\langle\phi ,-\Delta u \rangle=\langle \phi ,f\rangle$? im right? thanks