It's the Springer resolution; this works for all semi-simple groups. The resolution is the moment map from the cotangent bundle of $G/B$ to $\mathfrak{g}^*$. Look at section 6 of Ginzburg's notes.
Not to steal Mike's thunder, but there's an even more specific description of this resolution: given a nilpotent element $X$ of the symplectic Lie algebra, the fiber in this resolution over it is the space of complete flags $V_1\subset V_2\subset \cdots \subset \mathbb{C}^{2n}$ such that $V_i$ and $V_{2n-i}$ are symplectic orthogonal (this immediately implies that all the spaces in this flag are isotropic or coisotropic) which are preserved by $X$ ($XV_i\subset V_{i-1}$).
