Failover Cluster Role Properties dialog
This is same as 'Startup Priority' introduced in Windows Server 2012. You can set it from two places if you are using GUI. One what you have shown in the question and other one is below.  If you right click on any role name and click Change startup priority you will get to same options.

You can also use PowerShell to change the same setting. Example here.



Medium is the default priority. In the case of node failure, this priority setting determines the order in which roles are failed over and started on another node. A higher priority role both fails over and starts before the role of the next highest priority. If you assign the No Auto Start priority to a role, the role is failed over after the other roles but is not started on the new node. The purpose of startup priority is to ensure that the most critical roles have prioritized access to resources when they fail over to another node.

Ref:

Assigning role startup priorities