Balanced BST
For efficiency, we shall restrict the height of a BST so that it is $O(\lg n)$ instead of the worst-case $O(n)$.
Balancing to the rescue: The tree structure is adjusted as necessary to maintain a better balance and resulting height.
A BST is balanced when it has the following property:
For any node, the heights of the node's left and right subtrees are either equal or differ by at most $1$.
The above is often referred to as the balance property. A BST that maintains the balance property is a balanced BST or simply a BBST.