Bayḍah ordinarily means an egg, but here the speaker is not describing an actual egg. In classical poetic imagery it can suggest a delicate, protected woman of bright complexion. Khidr denotes a secluded or screened interior.
The construct bayḍati khidrin identifies the woman through an image of protected space. The image implies not merely color but distance, shelter, and restricted access.
ExpressionLiteral basisContextual effect
BayḍahEgg; image of whiteness and delicacyBeauty and delicacy
KhidrScreened placeProtected interior
Bayḍati khidrinGenitive constructCombined image of a secluded woman