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The formation conditions and the characteristics of quasilocal vibrations are analyzed in a realistic model of the crystal lattice at the microscopic level. Their evolution with an increasing impurity atom concentration has been studied. It is shown that the formation of the boson peaks is mainly due to the additional dispersion of high-velocity acoustic phonons. The dispersion is caused by the scattering of the high-velocity acoustic phonons of the basic lattice at quasilocalized vibrations localized on impurities. The similarity of the boson peaks in disordered systems and the first van Hove singularity in the regular crystal structures is demonstrated. The effect of the quasilocal vibrations and boson peaks on the low-temperature heat capacity and their transformation with an increasing impurity concentration is analyzed.