Hartshorn is a chemical leavener for cooking that was used before baking powder and baking soda became available.
It used to be made from the ground-up antlers of a hart (the term for a male deer.) It could also be obtained by distilling hair or decomposed urine. Later, it was chemically reproduced as ammonium carbonate.
Hartshorn is heat activated and therefore doesn't need anything to react with, just heat about 140 F / 60 C. This means that baked goods leavened with it don't have to be raced into the oven.
Hartshorn won't leave any alkaline flavour as baking powder or baking soda can sometimes. The downside to it was that any traces of it left in the baked good would leave a trace of an ammonia smell. It was therefore better used in small things such as cookies, crackers or biscuits where there was less batter for the gas Hartshorn produced to have to fight its way out of. North American style muffins, for instance, would be too big. For the same reason, it is not used for soft or moist cookies, as the gas would be trapped in them, but rather in dried ones that are meant to cook up crisp. The oven will smell like ammonia while the baking is happening.
Today, Hartshorn is a chemical, an ammonium salt derived from the carbonic acid called (NH4)2CO3, so you no longer have to fret about adding ground reindeer antler or dried urine into your cookie dough. It is sold either powdered or in lumps, which you have to crush yourself. The best chance of finding it in North America might be in a drugstore.
If you see a recipe that calls for it, it is an old recipe. It will appear largely in older German and Scandinavian recipes, particularly gingerbread cookies. It is often used in Lebkuchen, German cookies at Christmas. Cookies made with it are sometimes referred to as "Ammonia Cookies."
Some people say that it still makes some baked goods fluffier than baking powder can.
When used as smelling salts, is called "Salt of Hartshorn."
Do not substitute ordinary household cleaning ammonia.
It appears that Hartshorn was being used for a gelatin in the 1600 and 1700s, and that only at the end of the 1700s did it start to be used as a leavener.
Hartshorn was still being used as a source for gelatin up until at least the mid 1800s.