BCNF is the "Boss" rule.
The Rule: If you are powerful enough to determine another column's value, you MUST be a Key (a Boss).
The Violation: In a table of (Student, Course, Professor), where Student+Course is the key.
Suddenly, we realize: "Professor Snape ONLY teaches Potions".
So, knowing the Professor implies the Course.
(Professor -> Course).
But wait! Professor is not a Key. He's just a regular column. He shouldn't be bossing the Course around!
The Fix: Promote the Professor to his own table where he IS the key. (Professor -> Course).
Sometimes 3NF misses rare edge cases where a regular column controls a prime key. BCNF cleans up those last few anomalies.
Imagine a "Professor" column determining the "Subject". If Professor isn't a unique Key, this table violates BCNF. Make Professor a key in their own table!
"BCNF is strictly stronger than?"
3NF.