In European sets (ie mainland Europe rather than just UK) I have found that the use of covered jars is listed as for powder, pomade etc. I think the trinket jar is more of a British idea. I am not sure of this, so feel free to correct me, it's just what I've observed in studying covered jars.
They can also be covered candy dishes, or covered bonbon dishes. This piece could, in fact, be a covered candy.