Balanced means the tree's height stays close to the minimum for its node count, roughly log n. No branch is allowed to grow much longer than the others. Different schemes define the slack differently, but all cap how lopsided the shape can get.
Height matters because search, insert, and delete all cost time proportional to it. A balanced tree keeps those at O(log n). An unbalanced one can stretch into a chain, dragging the same operations toward O(n).
The danger is real with ordered input. Inserting sorted values into a plain BST builds a one-sided line, and it silently behaves like a linked list. Self-balancing trees fix this by adjusting shape as you insert and delete, trading a little bookkeeping for a height guarantee. That guarantee is what lets you promise fast lookups regardless of the order data arrives in.
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