I'd suggest taking a Q-tip , dipped in isopropyl alcohol , and swirling it around inside of your item , then smelling it to see if you can sense a fragrance/perfume ... if all you can smell is the alcohol , let it dry out for awhile & sniff it again .
If you do smell something like this , was prob. an aromatica as suggested by others .
Blackening on the inside of the upper portion (lid) would indicate incense burner - not so likely , since your item is made of wood .
Your item may also have had a base screwed to it's bottom (hole in the base might indicate this) to prevent tipping .
My 2 cents worth .