A voltage source maintains a constant Voltage across the output, and the current changes depending on load (up to the power supplies capacity).
A current source maintains a constant Current across the output, and the Voltage changes depending on load.
This concept is important for power distribution, because loads are NOT known and/or constantly changing. Also for rating of insulation.
Attempting to use a constant current source for a distribution system would result in power through a load varying as other loads would be added/removed from the total loading.
eg: In regards to motors, the motor would be spinning up and spinning down as other people turned their lights on. In the outer case, peoples lights would become very bright and/or be damaged if the motor was disconnected from the supply.
In another case, LED’s rely on constant power, and once they reach their threshold voltage and begin conducting current, the impedance of the LED actually drops resulting in Current increasing disproportionately (larger) than the increase of Voltage, which can damage the LED, and so a voltage source is not suitable for LED’s. Constant Current Sources are typically used for single point LED’s where a constant current is required to produce a constant lumen output.
Voltage Sources are most useful, because you can (trivially) create a small/basic constant current source from a higher rated constant voltage source, rather than the other way around.