cabinet, wardrobe, cupboard
橱 centers on a piece of furniture for storage: a cabinet, wardrobe, or cupboard where items are kept.
橱 combines 木 (wood) with 厨, which likely contributes the sound. The character is a phono-semantic compound indicating a wooden storage piece.
The wood radical 木 on the left suggests a wooden structure, and the right side 厨 looks like a kitchen or storage area. Picture a wooden cabinet in a kitchen for storing dishes.
For シュウ, imagine a shoe cabinet: shoe -> シュウ, and the wooden cabinet holds your shoes.