A max heap is a binary tree where the value of each parent node is greater than or equal to its child nodes, ensuring that the largest element is always at the root. In TypeScript, you can implement a max heap using an array, where the parent-child relationship is maintained by calculating indices: for a node at index i, its left child is at index 2i + 1, and its right child is at index 2i + 2. The key operations in a max heap are insertion (adding an element while maintaining the heap property) and heapify (ensuring the heap property is restored after removal or insertion). Max heaps are commonly used in priority queues, sorting algorithms (like heapsort), and in scheduling systems. Implementing a max heap in TypeScript not only solidifies your understanding of heaps but also prepares you for more complex applications of heap structures.