The energy band model

Individual atoms have multiple energy levels.
When atoms get closer, the energy levels get perturbed and splits into multiple energy states. A series of energy states form an energy band.

The formation of energy level, energy state and energy band vs. interatomic seperation. (William D. Callister and David G. Rethwisch, 2018) [Chapter 18.5]

Reference

William D. Callister, David G. Rethwisch, 2018. Materials Science and Engineering: An Introduction. Wiley Global Education.