The process priority property on a worklist item is strictly a visual identifier for users. It acts as an indicator for any user that they need to focus on one worklist item over another. There are no server based actions that come from setting the priority to different levels such as choosing one process over another to execute.
By design the K2 Server executes processes in a first in first out manner and usually does not get backed up or stuck on one process. (I say usually, because you never know what can happen) That being said, if you are perhaps running into issues with getting any process finished in a timely manner you may be lacking the infrastructure needed to fluidly run all of your processes. In this case the K2 server may be running at high/maximum capacity and you would need to look into adding another server to the farm or more hardware to your current server(s).
Below I have listed some documentation specifically on how you can manipulate or use the priority property when creating your processes:
Process General Properties Wizard:
http://help.k2.com/onlinehelp/K2blackpearl/UserGuide/current/webframe.html#B2.2_Process_General_Properties_Wizard.html#tracksearch=General process properties
Developer Reference for Priority property in the K2 API:
http://help.k2.com/onlinehelp/k2blackpearl/DevRef/4.6.11/default.htm#../Subsystems/RuntimeAPI/Content/topic11015.html
