What is the temporary basal feature in an insulin pump?

The insulin pump can increase or decrease the basal rate delivery for a period of time. This feature is NOT automatic. You have to choose how much more or less basal insulin you want (usually as a percentage of your normal basal rate) and for how long. Some automated insulin delivery systems allow you to use temporary basal rates in manual mode only and other systems allow you to use it in automated mode. 

When is this an advantage?

Examples of this feature would be for use during exercise, illness, or sleep, as your insulin needs may change.  When this is an automated feature in a closed loop system, the blood glucose target is adjusted according to the circumstances and the pump will make the basal adjustments. In a basic pump, learning how much to adjust the basal rate on your own can help prevent hypoglycemia and hyperglycemia.