A heap is a specialized tree-based data structure that satisfies the heap property, where the parent node is either greater than or equal to (in a max heap) or less than or equal to (in a min heap) its child nodes. This structure allows for efficient retrieval of the highest or lowest value, making heaps useful in algorithms like heap sort and for implementing priority queues. Heaps are commonly implemented using arrays, where the position of each element can be calculated based on its index. The first element is the root, and for any element at index i, its children can be found at indices 2i + 1 and 2i + 2. This organization helps maintain the heap property during insertions and deletions.