Curdling refers to an emulsion (such as milk, yoghurt, butter, mayonaise) that coagulates - usually because of some acidic compound (e.g. lemon juice or vinegar) or an enzyme (e.g. rennet in milk), and/or unusual temperatures.
After curdling/coagulation, 'curds' refer to the solids, 'whey' to the liquids.
Curdling is itself not a problem, and may be intentional, such as in the process of making things like cheese and curd.
Curdling has a bad association because of things like milk, where it is tied to the milk going sour(verify), and in some cases the texture may be less than pleasant, e.g. in mixed drinks.
The dairy-acid problem may be alleviated somewhat by adding some form of flour. The temperature one is often best solved by finding an alternative ingredient that will curdle at higher temperatures. Apparently, low-fat products are more likely to curdle(verify).