The space between the buccal and lingual cortical plates of the alveolar process is primarily occupied by cancellous bone.

- The alveolar process consists of two main types of bone: the outer cortical plates (buccal and lingual) and the inner trabecular bone.
- The buccal and lingual cortical plates are composed of compact bone, which is dense and provides strength and support.
- Between these cortical plates, the bone is less dense and forms a porous, trabecular structure known as cancellous bone (or trabecular bone).
- This cancellous bone contains marrow spaces and provides metabolic support and flexibility to the alveolar process, allowing it to withstand masticatory forces by absorbing stress.
- Woven bone is immature bone form, typically seen during bone repair or development, not a predominant component in the mature alveolar process.
- Lamellar bone refers to mature bone tissue with a highly organized structure, which can be part of both cortical and cancellous bone but does not specifically describe the architecture between the cortical plates.

Thus, the correct answer is cancellous bone, as it occupies the space between the dense outer cortical plates of the alveolar process.

Reference: R. M. Neville, D. Damm, C. Allen, J. Bouquot, *Oral & Maxillofacial Pathology*, Volume 1, Chapter 2, p. 45-47