Probably exactly what it says that the infant was deemed to die of fear. Today's diagnosis could be anything from cardiac arrest to shock to any number of other causes.
Depending on the period the records are from, and the wealth of the patients (which often determined the quality of the physician) you can find a wide variety of causes of death. Even leading into the 1900's I frequently find records where what we now call symptoms were listed as causes: vomiting, cough, sores, weakness, tremors. Then there are the more vague deaths such as "decline", "suddenly", and the occasional "unknown".
Unless it was something relatively well-known like small pox, cholera, and apoplexy, you will find many of the descriptions of cause of death to be imprecise, although some doctors may mention fairly specific conditions like cancer or St. Anthony's fire.
