An AVL tree is a type of self-balancing binary search tree that maintains a strict balance condition: the height difference between the left and right subtrees of any node cannot exceed one.

Named after its inventors, Adelson-Velsky and Landis, an AVL tree employs a balancing scheme known as AVL balancing. This technique ensures that the tree remains approximately balanced, thereby minimizing its depth. The depth of a binary search tree is crucial because it directly affects the efficiency of fundamental operations such as insertion, deletion, and searching. The shallower the tree, the less time these operations require.

To maintain balance, an AVL tree tracks the ‘balance factor’ of each node. The balance factor is defined as the difference between the heights of the node’s left and right subtrees. In an AVL tree, the balance factor for every node must be either $-1$, $0$, or $1$. If a node’s balance factor falls outside this range, it indicates that the tree has become unbalanced, necessitating a rotation operation to restore equilibrium.

There are four types of rotations used to rebalance an AVL tree: left-left, right-right, left-right, and right-left. The names of these rotations reflect the “heavy” side of the unbalanced subtree. For instance, a left-left rotation is performed when the left subtree of the left child of a node is heavier than allowed. These rotation operations are designed to rearrange the nodes in the tree, effectively reducing its overall depth.

When an insertion or deletion operation is executed on an AVL tree, the tree first performs the operation as a standard binary search tree would. Following this, it checks the balance factors of all affected nodes, starting from the newly inserted or deleted node and proceeding up to the root. If an unbalanced node is detected, the appropriate rotation operation is applied to restore the tree’s balance.

In summary, an AVL tree is an intelligent variation of a binary search tree that utilizes balance factors and rotation operations to maintain a near-balanced structure. This feature ensures that the tree’s depth remains minimal, thereby optimizing the efficiency of operations performed on it.