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We examine the origin of the formation of narrow bands in LK-99(Pb$_{9}$Cu(PO$_4$)$_6$O) and the parent compound without the Cu doping usingdensity functional theory calculations and model Hamiltonian studies. Explicitanalytical expressions are given for a nearest-neighbor tight-binding (TB)Hamiltonian in the momentum space for both the parent and the LK-99 compound,which can serve as an effective model to study various quantum phenomenaincluding superconductivity. The parent material is an insulator with thebuckle oxygen atom on the stacked triangular lattice forming the topmost bands,well-separated from the remaining oxygen band manifold. The $C_3$symmetry-driven two-band TB model describes these two bands quite well. Thesebands survive in the Cu-doped, LK-99, though with drastically altered banddispersion due to the Cu-O interaction. A similar two-band model involving theCu $xz$ and $yz$ orbitals broadly describes the top two valence bands of LK-99.However, the band dispersions of both the Cu and O bands are much betterdescribed by the four-band TB model incorporating the Cu-O interactions on thebuckled honeycomb lattice. We comment on the possible mechanisms ofsuperconductivity in LK-99. even though the actual T$_c$ may be much smallerthan reported, and suggest that interstitial Cu clusters leading to broad bandsmight have a role to play

Effective tight-binding Hamiltonian for the low-energy electronic structure of the Cu-doped lead apatite and the parent compound