A local maximum is a point in a mathematical function where the value is higher than the values of its immediate neighbors. In simpler terms, if you imagine a hilly landscape, a local maximum would be like the top of a small hill, where the height is greater than the surrounding areas. Local maxima are important in various fields, including optimization and machine learning. They help identify the best solutions within a limited range, but they may not represent the absolute highest point, known as the global maximum. Understanding local maxima is crucial for analyzing functions and making informed decisions.