Nursery ponds provide a relatively safe and closely-monitored environment for baby fish to grow up in. Before fish grow their defensive scales and fins, they are particularly vulnerable, especially when they're the perfect size for their larger neighbors to snack on. Separating them from larger fish gives them a better chance of survival. You'll typically see nursery ponds used for fish going through the fry to fingerling stages of life.
Infant fish are particularly sensitive to stressful conditions within the water, which can range from poor oxygen levels, high concentrations of waste and debris, or inappropriate temperature/ph levels. A separate, smaller tank allows for more individualized and consistent monitering than the larger growing tanks. Later on, fish are more resistant to changes in their environment, and won't need as much oversight.