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CurrentCase is an element parameter in the set AllCases (which itself is a subset of Integers), and its value indicates which case is loaded currently. 

CurrentCase — AIMMS Function Reference

For example, if you have 5 different case files saved in the data folder of your AIMMS project - each of these 5 case files represent the element 1, 2, .. 5 in the set AllCases. 

Active case in the status bar of AIMMS Developer shows the name (path) of the case file that is loaded. This would typically be the value of CaseFileURL(CurrentCase)

CaseFileURL — AIMMS Function Reference

Hope this helps.