Ive never noticed this column before, and am surprised it isnt in the default view, but if you run the standard running instances query in the BizTalk Administration Console it lists the running instances currently within your BizTalk Group.
If you want to know which server within your group an instance is currently executing on then you can add additional columns to this query, one of which tells you the server which is currently being used by each instance. See diagram below:
What would be nice also is if in HAT it also recorded which server each orchestration shape and message instance had executed on. This would help significantly in troubleshooting some instances.