Grading of Clifford algebra

Question

Given a vector space $V$ and a quadratic form $q$ on it, we know that the Clifford algebra $Cl(V,q)$ is a graded algebra, which is a property inherited by the Tensor algebra $T(V)$. Unless in the trivial case $q\equiv 0$, $Cl(V,q)\not\cong T(V)$ as algebras, but I've read that the associated graded algebra is isomorphic to $\Lambda(V)$, because the ideal by which $Cl(V,q)$ is constructed involves terms of degree 2.
Why is the isomorphism true? What does it means the associated graded algebra in terms of Clifford algebra $Cl(V,q)$ and which informations can I get by this?
Thank you all.