Lean meat has less fat.
This furniture uses the heartwood part.
脂身 is the fatty part of meat, while 赤身 is the lean, non-fatty part.
赤身 refers to red, lean fish or meat, contrasting with 白身's white, milder flesh.
赤身 is the lean, red meat of tuna, while とろ is the fatty, marbled belly cut.
Compound of 赤 (red) and 身 (flesh/body). The wood sense is a metaphorical extension of the color contrast.