A theory $T$ is consistent iff there's no sentence $\varphi$ s.t. $T \vdash \varphi$ and $T \vdash \neg\varphi$.
A theory $T$ is sound iff all its axioms are true.
I can see why soundness implies consistency, since if all the axioms of a theory are true, and suppose the theory has a truth-preserving proof system, then every statement that can be derived from our theory must be true. There's no way we could derive a contradiction or a false sentence.
I'm not quite sure why consistency doesn't imply soundness. Do I have to show that there could be a consistent theory $T$ which has a false axiom?