A meromorphic function is a type of complex function that is defined on an open subset of the complex plane, except for a set of isolated points called poles. At these poles, the function can approach infinity, but it remains well-defined and finite elsewhere. This means that meromorphic functions can be thought of as rational functions, which are the ratio of two polynomials, except they may have certain points where they are not defined. Meromorphic functions are important in complex analysis and have applications in various fields, including mathematics, physics, and engineering. They are closely related to analytic functions, which are functions that are differentiable everywhere in their domain. The study of meromorphic functions helps in understanding the behavior of complex functions and their singularities.