The high priority refers to the message not the passenger. i.e It is of great importance this message gets delivered.

Theoretically there are two levels: High Priority and Normal. High Priority will inhibit boarding until it is acknowledged and is for seat changes (including upgrades) or could be manually entered by an agent.

Normal priority in Amadeus will just display when the passenger boards, but allow the agent to continue boarding. In BA's FLY system though, Normal priority behave identically to High Priority comments.