A binary search tree (BST) is a specialized tree data structure that facilitates efficient searching, insertion, and deletion operations. In a BST, each node contains a value and has at most two children: a left child and a right child. The key property that defines a binary search tree is that for each node, the values in its left subtree are less than the node's value, while the values in its right subtree are greater. This property allows for efficient searching, as it reduces the search space by half with each comparison, resulting in average-case time complexity of O(log n) for search operations, where n is the number of nodes in the tree. Inserting a new value into a BST involves navigating through the tree, starting from the root, and comparing values to find the appropriate position for the new node while maintaining the BST properties. Deletion operations can be slightly more complex, especially when removing nodes with two children, as it requires finding a replacement node (typically the in-order predecessor or successor) to maintain the tree's structure. Binary search trees are widely used in various applications, such as database indexing, memory management, and implementing associative arrays. However, BSTs can become unbalanced, leading to degraded performance (O(n) in the worst case) when elements are inserted in sorted order. To mitigate this issue, self-balancing binary search trees, such as AVL trees or red-black trees, can be utilized to ensure balanced height and maintain efficient operations.