The right to undergo salary arbitration is governed by Article 12 of the most recent collective bargaining agreement between the NHL and NHLPA. Players, mainly restricted free agents, utilize this tool because it is one of the few bargaining tools available to them.
The whole process is a bit too long and complicated to explain in full here, but the short story is that players can only undergo salary arbitration once during their career; meanwhile, teams can still negotiate with players until their arbitration date, usually set in late-July to early-August.
A few factors that are taken into account during the arbitration process include a player’s overall contribution to the team, length of service to the team and the NHL, overall performance and stats throughout previous seasons, and injury/illness history.