Count is normal aggr function, where you can count ant field, like
Count(EmployeeId) it will give you number of employees.
where getpossiblecount() works with selection, when you select a field, you see possible values for that field,
let say you select Department in list box, and on selection of Department you can see how many employees are in selected department, so you can use getpossiblecount() for the counting purpose. it will give you all employee for that selected department.
Hope it helps...
GetPossibleCount() is exactly the same as Count(distinct total ...). Note the total qualifier - this means that the function isn't sensitive to the dimensional scope. See more on http://community.qlik.com/blogs/qlikviewdesignblog/2013/09/09/aggregation-scope
The GetPossibleCount exists as a "sister" function to GetSelectedCount and GetExcludedCount.