To anneal metal jewelry is to heat it to a set temperature for a set time with the goal of removing all stress points and hardenings. Annealed rings are then easier to open and less brittle, though they tend to hold beads more weakly than hardened jewelry in the smallest gauges.
To anneal a metal, one must bring the temperature of the metal up to half its melting point, which is usually done in a vacuum chamber. Then, the metal is allowed to cool down. This will re-align the crystal structure within the metal to allow something such as a captive bead ring to bend more easily, as well as remove surface contaminants, such as free nickel in stainless steels. Annealing is part of the process 316LVM stainless steel undergoes to meet ASTM F-138 specifications.