The term 'Big Name in Fine China' refers to two well-known brands of china, Lenox and Spode. Lenox is an American brand of fine china that was founded in 1889 and is known for its intricate designs and high quality. Spode is a British brand of china that has been around since the late 18th century and is renowned for its classic blue and white designs. Both Lenox and Spode are highly sought after by collectors and connoisseurs of fine china.