'Always Give a Reason Why' - How to describe this subject area?
This particular study, sometimes called the "Xerox Experiment", was done by Ellen Langer, who studies "mindfullness", but that may not be what you are looking for.  It is also cited on Wikipedia under Attitude Change - Heuristic Processing:


  For example, people are more likely to grant favors if reasons are
  provided. A study shows that when people said, "Excuse me, I have five
  pages to xerox. May I use the copier?” they received a positive
  response of 60%. The statement, “Excuse me, I have five pages to
  xerox. I am in a rush. May I use the copier?” produced a 95% success
  rate.


It is worth noting however, that a study published in the same year by Stanley Milgram (famous for his obedience experiments in the 60's), cited on Wikipedia under "Breaching Experiments", about people giving up their seats in the subway found a similar success rate when no reason was given, but a significantly lower compliance rate if a trivial reason was provided:


  the second condition, the trivial justification ... a much lower number gave
  up their seats.


A related field that a layman might find more accessible, is called "behavioural economics", and there is also a lot of overlap with "cognitive bias".  Search YouTube for Dan Ariely, you'll learn lots of neat tips and tricks just like this one, backed by peer-reviewed studies, about how easily people can be manipulated.