For the heuristic but naïve geometric meaning, one can imagine that $\mathcal{D}$ is the derived Fukaya category, $K(\mathcal{D})$ is the sublattice of $H_{n}(X)$ generated by the Lagrangians, the central charge is $Z(L)=\int_{L}\Omega$, the subcategory $\mathcal{P}(\phi)$ is generated by the special Lagrangians of constant phase angle $\theta=\pi\phi$, the Harder-Narasimhan decomposition means a multiple Lagrangian connected sum with decreasing phase angles

$$L\simeq L_{1}\#L_{2}\#\ldots\#L_{N},$$

and the calibration property comes from the fact that the total mass of a special Lagrangian is equal to $|Z(L)|$, and the mass bounds any norm of $[L]\in H_{n}(X)$ using Poincaré duality, assuming $H_{n}(X)$ is finite dimensional.