I have seen many descriptions of Boyce-Codd Normal Form, however none make any sense. Can somebody explain this in easy terms?

R(supplier_id, part_id, supplier_name, qty)

Keys:

(supplier_id, part_id)
(supplier_name, part_id)

The following constraint is given:
supplier_id => supplier_name, supplier_name => supplier_id

Therefore the relation R does not violate 3NF, however it violates BCNF.

To solve:

R1(supplier_id, part_id, qty) key (supplier_id, part_id)
R2(supplier_id, supplier_name) key (supplier_id), UNIQUE(supplier_name)