A binary heap is a complete binary tree that maintains a simple ordering between parents and children. Two properties define it together, and both must hold at all times.
The shape property says the tree is complete: every level is full except possibly the last, which fills left to right. That compact shape lets you store it in a plain array with no pointers.
The heap property is a parent-child rule. In a max-heap, every parent is at least as large as its children, so the largest value sits at the root. A min-heap flips it, keeping the smallest at the root. The rule only relates parents to their own children, not siblings to each other, so the heap is far weaker than a sorted order. That weakness is the point: it makes reading the top element O(1) while keeping inserts cheap.
Rewriting in plainer words…
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