Area Scouts work for a specific MLB team and have responsibility for a particular geography (i.e., a couple of states or some fraction therein).
Their primary responsibility is to know the HS and College prospects in their territory and to observe, report and communicate with them and their families as interest grows. They will also assemble workouts or high prospects in their territory and work with their club to ensure the correct people from their organization are in attendance at those workouts.
Area scouts typically distribute the player questionnaires and will sometimes administer various tests to prospects (vision, reaction/reflex, personality, etc).
They also coordinate and lead home visits.
During the HS season, they run herd over the schedules of their prospects for their team and will work to ensure that they get their crosscheckers and senior scouts in town where and when the prospects are playing.
When all is said and done, they should know where and when the top prospects in their territory are playing. They are the initial and key contact between player/family and their MLB club for getting and giving information. Their job is to know the prospects at a personal level better than anyone else in their organization and to be able to lobby for or alert red flags for their team come draft time.
That's a pretty high level overview, but probably captures their key responsibilities.