Without symbols:
1NF: one value per cell.
2NF: every non key column depends on the whole key. If key is (student_id, course_id) and student_name depends only on student_id, that's a partial dependency, move it out.
3NF: a non key column shouldn't depend on another non key column. If you store pincode and city, city depends on pincode, not on the key. Move it out.
BCNF: stricter 3NF, every determinant has to be a candidate key. Only shows up when there are overlapping candidate keys.
The line people use: "the key, the whole key, and nothing but the key".