As i wrote in comment, you need only
CountIf
worksheet function. But if you would like to do it with VBA code, OK, i'll show you an example. Below code is to use when both excel files (master and current) are opened.
Copy the code below and paste it into master file in new module :
Dim srcwsh as Worsheet, dstwsh As Worksheet
Dim i as Integer, j As Integer, counter as Integer
Dim sAppName As String
Set dstWsh = ThisWorkbook.Worksheets(1)
Set srcWsh = Application.Workbooks("current.xls").Worksheets(1)
counter = 0
i = 2
j = 2
Do While srcwsh.Range("A" & i)<>""
sAppName = srcwsh.Range("A" & i)
Do While dstwsh.Range("A" & j)<>""
If dstwsh.Range("A" & j) = sAppname Then counter = counter + 1
Loop
srcwsh.Range("B" & i) = counter
counter = 0
Loop
This is not optimal code, because it compares data row by row (cell by cell), but it shows "logic".