Define an AVL tree and its balancing techniques.

An AVL tree is a self-balancing binary search tree where the difference between heights of left and right subtrees cannot be more than one.

An AVL (Adelson-Velsky and Landis) tree is a type of binary search tree which maintains its balance through a scheme known as AVL balancing. This balancing technique ensures that the tree remains approximately balanced, meaning that the depth of the tree is kept to a minimum. This is important because the efficiency of operations on a binary search tree (like insertion, deletion, and searching) is directly related to the tree's depth. The shallower the tree, the less time these operations take.

The balance of an AVL tree is maintained by tracking the 'balance factor' of each node. This balance factor is the difference between the heights of the node's left and right subtrees. In an AVL tree, every node's balance factor must be -1, 0, or 1. If the balance factor of any node is not in this range, a rotation operation is performed to restore the balance.

There are four types of rotations used in AVL balancing: left-left, right-right, left-right, and right-left. The names of these rotations describe the 'heavy' side of the unbalanced subtree. For example, a left-left rotation is used when the left subtree of the left child of an unbalanced node is heavy. The rotation operations are designed to shift nodes around in the tree to reduce its depth.

When an insertion or deletion operation is performed on an AVL tree, the tree first performs the operation as a standard binary search tree would. Then, it checks the balance factors of all nodes, starting from the newly inserted or deleted node and moving up to the root. If it finds an unbalanced node, it performs the appropriate rotation operation to restore the balance.

In summary, an AVL tree is a clever variation on a binary search tree that uses a balance factor and rotation operations to maintain a roughly balanced tree. This ensures that the tree's depth is kept to a minimum, which in turn ensures that operations on the tree are as efficient as possible.