Are gap semesters frowned upon in graduate school applications? Should I explain mental health situation that led to the gap?
I'm going to give a slightly different advice from the previous answers.  I don't want to counsel dishonesty here, but I think it would be very unwise to write anything in your personal statement that suggests any mental health problems, especially if the only thing that needs explaining is taking a semester off.  

I want to emphasize that I think the stigma around mental health problems is very unfair and based on ignorance.  However, the people reading these applications will have probably internalized it to some degree: if you, for example, mention attempting to commit suicide, that will be the most vivid and memorable thing from your application, whereas your master's degree ending a semester early will be barely noticeable.  I think you will probably be fine not mentioning it at all, but if you do, I would just say it is for health reasons, or to prepare for moving to another country (which are, of course, true).  One of the primary things an admissions committee will have in mind is whether a student is capable of finishing the program, while not creating a lot of trouble for people in the department. They have had pain-in-the-butt students before, and would really prefer to avoid having any more.  Mentioning "personal and social challenges" or "excruciating circumstances" (which, incidentally, sounds very strange in English; it's hard to imagine what you really mean by it) is not going to give them confidence that you won't make a lot of trouble for them.