Visualize BST insertion step by step. Watch a new value walk down the tree to its correct position while maintaining the BST invariant.
Follow the same path as search, but instead of returning when null is reached, create a new node there.
Starting at root, compare the new value to each node. Go left if smaller, right if larger, just like search.
When you follow a left/right pointer that is null, that is where the new node belongs.
Insert the new node at the found null position. BST property is maintained because we followed value comparisons the entire way.
Plain BST insert does not rebalance. This can degrade to O(N) for sorted input. Self-balancing trees (AVL, Red-Black) fix this.
After each insert the tree may become unbalanced. The visualization lets you insert a value and watch it walk down the tree to its correct position.