As you gain AVP, the Initiative’s primary objective progresses and the Nexus gains levels. Gaining Nexus Levels rewards you with Cryo Pod Perks (comparable to your personal skill points). The Nexus Level caps at 20. At the level cap, you can purchase and unlock all available Cryo Pod Pperks (provided you’ve accumulated enough per-planet Viability for certain perks).
Unrelated to Nexus Level, parts of the Nexus expand upon reaching certain points in the main story (such as the tech lab and the Vortex Bar opening up after Ryder activates the vault on Eos).