I know the distinct. Without the aggr(), I could use it for [Request ID] 1 and it would work but then if I don't select the request ID and I have 2 time the same measures for 2 different request ID, then I don't want the distinct on it.
Aggr ignores dimensions. So if you want an expression to calulate using dimensions that aren't present in your table or you want to calculate something using only the first 2 dimensions in your report and not all 3, you would use aggr. Essentially you can build an entire straight table with no dimensions using aggr and still get the values you want. It is a resource intensive function, so use with caution on 'big' data sets
To answer your second question and using the above explanation
Aggr(DISTINCT Sum([Measure Service]),[Request ID],[Serivce ID]). Literally just add the dimension that has the logic you want to apply when summing the values you deem distinct