As Chuck told. But maybe you are asking for more visual example - imagine, that you are creating robot with a microprocessor and some motors.
You know, that the microprocessor needs a constatn voltage to work correctly (usually 5V, or 3.3V - depending on the exact type). On the other hand the motors would need no power, when your robot is standing still, but would need a lot of power for the robot to drive fast to the hill. So you need source, which provides those 5V regardless of what current is taken from it, be it some mA when the robot is still and the processor just waits for your commands, or couple of Amperes, when you command it to run fast to hill. Such source is called Voltage source, as it keeps the same voltage, regardless how much current you take from it.
On the other hand the LED needs specific current to shine as much as it can, but not be destroyed. And different LEDs of the same kind little differs in characteristics, while different kinds of LEDs differs wildly (some works best around 2.5V, others at 0.6V). So if you are building source for illuminating something with LEDs, you want it supply only so much current, that LEDs can manage safely (usually around 20mA) regardless of Voltage which it tooks. Especially, if you want to connect those LEDs in series. And if you want to connect different number of them each time. You still want just 20mA current per branch.
Such source would provide just the right current, regardless of which voltage it needs to force that current thru and so it is called Current source.
If you change them, than it will result in dissaster - when your robot would stop, only microprocessor would consume energy and Current source would try increase the Voltage high enougth to ensure the same Amperes are forced inside, as they was when the motors drive the robot to the hill. The only way to have the current the same is to increase Voltage really high (like thousand volts) and it would destroy the microprocessor instantly.
On the other hand, if you connect long line of LEDs to Voltage source, which would provide voltage exactly as high as needed to force 20mA thru and then changed your mind and attached just half of those LEDs, then the Voltage source would keep the same Voltage and the current would not be 20mA as needed, even not 40mA which would destroy those LEDs, but as each LED just substract constant voltage, then there would be effectively such current, that the remaining voltage would be distributed over wires (and source internal resistence), which means a lot of Amperes and your LEDs would literally burn instantly in flame.
So you need the right kind of source for the right kind of work.
- Voltage source keeps Voltage the same even if it means to provide different current into the circuit, (if the circuit resistance would change) and have easiest time when nosting is connected, as it have no need to provide any curreent at all
- Current source keeps Current the same, even if it means to provide different voltage. And will be more happy with just wire between connectors, as it means nearly no voltage to provide for reaching demanded current.
(Of course real sources cannot go to extreme values, so if you take more and more power, than you reach the limit, where they can regulate and they else shut down, or burn or provide less, then they should.)
And with the right circuit you can (to some level) change one type of source to another.
For example if you connect resistor in serie with your load on Voltage source, then the resistor would limit how much current can go to the load (if the load is shortcuted, then all voltage is on the resistor and so the current is not higher, then I=U/R - it is used for LEDs in many schemas - there is resistor near them limiting the maximal current, even when it means the LED is not at its total optimum).
On the other hand if you take Current source and shortcut it with low resistor, then the maximal voltage there would be U=IR and if you connect in paralel any load (usually with a lot higher resistence than R), than the current is divided into both branches, but mainly goes thru the small shortcut R and the voltage over the load is limited to the U maximial, but less if the load takes more current thru it. It is used for Amper Metters, where you let go the main current thru piece of wire and measure the voltage over the piece of wire with voltmeter (with usually really high resistence) so you can count the current with the formula U=IR (we know the R and measuerd the U), so I = U/R (where the U is voltage lost over the shortcut wire and R is resistence of the wire)