Monoclinic BiB3O6 is an excellent nonlinear optical material with many advantages compared to other borate crystals. The origins of the optical effects and the chemical stability of BiB3O6 are studied with gradient-corrected hybrid B3PW density functional theory within the Gaussian-orbital-based CO-LCAO scheme. Including spin-orbit coupling, the B3PW hybrid functional provides an estimate of the indirect band gap of 4.29-4.99 eV closer to the experimental value of 4.3 eV than HF, LDA, or GGA. The crystal orbital overlap population to give a detailed first-principles analysis of chemical bonding and the density of optical absorptions by convoluting the occupied density of states and the virtual density of states have been calculated. Obvious Bi-O covalent bonds have been found with different energy ranges for 6s-2p and 6p-2p interactions. The reason that [BiO4](5-) units are mainly responsible for the optics of BiB3O6 in the long-wavelength region is due to the electronic transfer from occupied O 2p to empty Bi 6p orbitals favored by the Bi-O covalent bonds. The relativistic and correlation effects lead to fundamental differences of the band structure, chemical bonds, and optical effects for BiB3O6 compared with nonrelativistic and uncorrelated calculations.