I acquired this in an auction job lot several years ago and I've never been able to figure out what it is. It is obviously very well made with a lid that fits perfectly. It has a very clear mark (last pic). The hole in the top has dirt around it suggesting there might have been a burning wick but the inside appears clean.
perhaps an oil wick lamp; this sort allows for easy refills by lifting off the top. examples: (2) Ceramic Oil Wick Lamp/Lights | Mercari Shanware Oil Lamps Buy Best Selling Handmade Pottery Oil Lamp Indoor - Orange Flower ☆ Burns 4-6 Hrs and Easy to Refill with Paraffin Oil or Other Lamp Oil ☆ Reliable and Safe Candle Flame. Wick is Easily Adjustable for Oil Candle Flame Strength in Cheap Price on Alibaba.com
I forgot to put in the dimensions. It is 4" across the bottom and a bit over 4" high - seems too large for perfume or incense. TallCakes suggestion of an oil lamp may be the answer but those lights are more decorative - mine is more utilitarian. Does anyone recognize the mark on the bottom?