The "decreasing key" operation is commonly used in data structures like heaps to reduce the value of a specific element. This operation is essential in maintaining the properties of the data structure, especially in a min-heap, where the smallest element must always be at the root. By decreasing the key, the element's new value is adjusted, and the structure is re-ordered to ensure that the heap properties are preserved. To perform a decreasing key operation, the element's value is updated, and then a process called "heapify" is applied. This process involves comparing the updated element with its parent and potentially swapping them until the heap property is restored. This operation is crucial in algorithms like Dijkstra's algorithm, where it helps efficiently manage priority queues.