What is a depletion layer? What is the order of its thickness?

(N/A) depletion layer (or depletion region) is a region formed at the $PN$ junction where the mobile charge carriers (electrons and holes) have diffused across the junction and recombined, leaving behind immobile ionized donor and acceptor atoms.
Because this region is devoid of free charge carriers, it acts as an insulating layer that prevents further flow of current across the junction under equilibrium conditions.
The order of the thickness of the depletion layer is typically $10^{-6} \, m$ or $1 \, \mu m$.