Source : Webster's Revised Unabridged Dictionary (1913)

, to laugh secretly, or so as not to be observed, especially
while apparently preserving a grave or serious demeanor toward
the person or persons laughed at.

   {To laugh out}, to laugh in spite of some restraining
      influence; to laugh aloud.

   {To laugh out of the other corner} (or {side}) {of the
   mouth}, to weep or cry; to feel regret, vexation, or
      disappointment after hilarity or exaltation. [Slang]