A low power application is an embedded system or circuit where amount of power used is very low. The power is electronic is measured in Watts. So for eg. if a system uses 1W of power and another same system uses 2W of power, so the system with 1W of power usage is low power system.
Now power in electronic system is multiplication of applied voltage and current through circuit i.e.
P = V*I
So in a way, the power usage is directly proportional to both voltage and current keeping another entity as constant. So, if u have designed a system of spec A with 5V and 10mA current and same system with better components to reduce current usage to 1mA keeping supply constant at 5V. The power used by 1mA is 5mW and by 10mA is 50mW, so 5mW system is low power. But at any instant, either or both voltage and current can be low.
Most of systems today use 3.3V and lesser compared to 5V, so using low voltage automatically reduces power. Also, the improvement is made in terms of current consumption to very minimum which also reduces power usage.
Hope that helps.