"It is your coat."
Translation:Det är din rock.
At the point that you are saying "It is"... the coat hasn't been mentioned so it is still a mystery item. When the item is unknown (ie hasn't been mentioned yet), we use Det.
Once the item is known, we use den/det depending on the gender of the item you're referring to.
So you could say: "It is your coat. It is black." Det är din rock. Den är svart. You say DEN är svart, because you are referring back to a known item (your coat).
Another way to explain it....... by saying: "Det är din rock. Den är svart" ... What you are effectively saying is: "This mysterious unknown item is [cue the fanfare, wait for the big reveal]... your coat. The coat we've just told you about is black."
Does that make sense?