The Bergman kernel is a mathematical tool used in complex analysis, particularly in the study of several complex variables. It is a reproducing kernel associated with the space of square-integrable holomorphic functions on a bounded domain. This kernel helps in understanding the properties of these functions and their behavior within the domain. In practical terms, the Bergman kernel allows mathematicians to express functions in terms of an inner product, facilitating the analysis of function spaces. It plays a crucial role in various areas, including theory of several complex variables and functional analysis, providing insights into the geometry of complex manifolds.