A local minimum is 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. Local minima are important in various fields, including optimization and machine learning. When algorithms search for the best solution, they may get stuck in a local minimum instead of finding the global minimum, which represents the best possible outcome. This can affect the performance of models like neural networks and gradient descent methods.