Tucker decomposition is a mathematical technique used in tensor analysis to break down a multi-dimensional array, or tensor, into simpler, lower-dimensional components. It represents the tensor as a core tensor multiplied by a matrix for each mode, allowing for efficient data representation and analysis. This method is particularly useful in fields like machine learning, signal processing, and data mining, where high-dimensional data is common. By reducing the complexity of the data, Tucker decomposition helps in extracting meaningful patterns and features, making it easier to work with large datasets.