A heap is a specialized tree-based data structure that satisfies the heap property, which can be either a max-heap or a min-heap. In a max-heap, each parent node is greater than or equal to its child nodes, while in a min-heap, each parent node is less than or equal to its child nodes. This structure allows for efficient retrieval of the highest or lowest value, making heaps useful in various applications like priority queues. Heaps are commonly implemented using arrays, where the parent-child relationships can be easily calculated using index positions. The root of the heap is always at the first index, and the children of a node at index i can be found at indices 2i + 1 and 2i + 2. This efficient organization makes heaps a popular choice in algorithms such as heap sort and for managing priority queues.