The smoking cap is a hat designed to be worn indoors, whilst not Victorian in origin that is the period I mostly associate with them.
Smoking Cap is pill box hat that is usually worn with a smoking jacket which is thick short velvet or silk jacket.
They were worn by high class gentlemen while drinking port or brandy and smoking Turkish cigarettes & cigars home, both the cap and jacket where worn to stop normal cloths and hair smelling of smoke, they also keep the head warm.
The decorated smoking caps as I'm wearing here is a result Victorian men's sweethearts using their leisure hours to stitch and embroider these caps whilst they were fighting in Crimean war.
Smoking caps became high fashion after dinner wear in the Victorian period, today they are making come back with men and women, however someone has suggested they should now be called the more politically correct 'Leisure Cap'.