I can understand that you are somehow puzzled by the Past Perfect being the correct tense in this case, because we have learnt that for an action which started at an unspecified point in the past the Present Perfect is the correct choide.
Nevertheless, if you look really close you'll see that there is a specific point in the past before which the action had taken place. And that past point is when Jean came to America. And relative to that point in time we have an action which occured even further back in time: Jean's studying Englisn.
In a shutshell, whenever we have a action which started before a past action or moment and which was completed by the that moment, we use the Past Perfect,
e..g: [i][b] "Before Jean came to America (=action/time in the past), he had studied (or: had been studying) English for six month (=action preceding the past action/time)."[/b][/i]
The Gerund form (" before coming" ) in the original sentence is only anotther form (a reduced form) of saying "before he came".