Literally, the formation of curds, a byproduct of the first stage of cheese production, often rich in casein. More technically, curdling is the process by which proteins and fats in milk begin to coagulate into a solid substance within the mixture of milk and rennet. When looking for a technical definition of the term or a culinary definition, this is probably what you’ll find.
Now, even more technically, curdling is the process by which solidified compounds separate out of an emulsion and or colloid, away from the liquid of the compound. When someone says that an emulsion is breaking, the emulsion is technically curdling. If you’re wondering if that means that cow’s milk is an emulsion, that’s exactly what it means. Cow’s milk, and other dairy milks, are examples of naturally occurring emulsions.
Now, I did focus on the use of rennet, a type of enzyme, as a component of curdling. However, enzymes are primarily meant to speed up a reaction. With sufficient energy, such as heat from a pan, you can denature the proteins inside the emulsion, causing them to unfold and begin the curdling process.
Aside from cheese making, there is at least one other reason why you would make use of curdling. If you are producing a form of tofu, then you will want the mixture to curdle then as well. On the topic of uses, though, there is its counterpart: when to be weary of curdling.
Any time you are preparing anything with milk, there is a chance that you could cause the milk to curdle. If that happens, say in a cream based sauce or in a custard, you will end up with a lumpy texture and an unpleasant flavor.