A local minimum refers to a point in a mathematical function where the value is lower than the values of its immediate neighbors. In simpler terms, if you imagine a hilly landscape, a local minimum would be like a small valley that is lower than the surrounding hills, but not necessarily the lowest point in the entire landscape. In optimization problems, finding a local minimum is important because it can represent a solution that is good enough for practical purposes. However, it may not be the best possible solution, known as the global minimum, which is the absolute lowest point across the entire function.