1.
dry cough
A cough that produces no phlegm. A non-productive cough.
2.
fake cough; deliberate cough
A cough made on purpose to get someone's attention, signal discomfort, or cover an awkward silence.
空咳 has two distinct meanings: a dry cough (medical) and a deliberate cough (social).
Forms
The prefix 空 means "empty" or "lacking content," as in 空っぽ (empty) and 空振り (a swing and a miss). Here it indicates a cough with no phlegm, or a cough with no real need to cough.
Medical sense
A dry, non-productive cough. Contrasts with 痰の絡む咳 (a productive cough with phlegm). Common with colds, allergies, and dry air.
Social sense
A deliberate cough used to get attention, signal discomfort, or break an awkward silence. The standard expression is 空咳をする.