Hibernation is minimal activity plus a reduction in metabolism.
Metabolism is the collection of chemical reactions that keep an animal alive, including processing nutrients, maintaining cells and producing energy. During hibernation, an animal actively suppresses its metabolic rate to reduce the energy required to survive periods when food is scarce.
This suppression usually occurs alongside lower body temperature, slower breathing and a reduced heart rate. The changes are linked: a cooler body generally requires less energy for maintenance, while slower physiological processes reduce fuel consumption. Animals may survive for days, weeks or months by using stored body fat or cached food.
Respiration and circulation also slow during hibernation, so they are related effects rather than the best answer to the question. Digestion may largely pause, but it is not the defining biological process being reduced. Modern definitions emphasize metabolic suppression, even for animals such as bears whose body temperature does not fall as dramatically as that of small rodents.
Hibernation is distinct from ordinary sleep: it is a controlled seasonal state involving broad physiological and metabolic changes.