The `std::exception` class is a part of the C++ Standard Library, designed to handle errors and exceptional situations in a program. It serves as the base class for all standard exceptions, providing a consistent interface for error handling. By inheriting from `std::exception`, other exception classes can define specific types of errors, allowing developers to catch and manage different exceptions effectively. When an error occurs, an object of a derived exception class can be thrown using the `throw` keyword. This object can then be caught using a `try-catch` block, enabling the program to respond appropriately without crashing. The `what()` member function of `std::exception` returns a description of the error, aiding in debugging.