These current controls are on DC powers supplies that can operate in both constant current and constant voltage modes. Constant voltage is where the supply changes the current through a variable load to maintain a constant voltage at the output connectors (or, on some supplies, at the remote sensing terminals). Constant current is where the supply varies the voltage across a variable load to maintain a constant current through the load.
I find I use constant current mode as much or probably more than constant voltage. Here's an example -- suppose you want to measure the voltage-current relationship of an LED. The maximum rated current through the LED is 700 mA, so you know you don't want to exceed that. The way I usually make the measurements is to set the constant current knob to a low current -- here, let's start at 50 mA. Then turn the voltage knob way up. Connect the LED and 50 mA will be flowing through it. Read the voltage from the power supply that is the voltage at the output terminals (or use a separate voltmeter). Then set the current to 100 mA, and repeat. Continue up to the rated current of the LED. Now you have your data and can e.g. plot it or decide where you need a bit more resolution.
This i-V relationship can also be generated with a constant voltage power supply. You just have to keep your eye on the current and not let it exceed the rating of the LED.
In the 1980's, HP made a nice little current source with 25 mA and 250 mA full scale current; I think the compliance voltage was near 80-100 V. It had a nice 10 turn pot to adjust the current with a turns counter on it. This was quite a handy power supply to have in the lab.
When I'm using the DC supply in constant voltage mode, I'll often set the current setting to a value that I want to limit the current to in case of a short circuit or low impedance. For example, when powering up a new circuit on a prototyping board, I'll know about what the power supply current should be. I set the current limit to this value. Then, when I start turning up the voltage to power the circuit for the first time and I see the LED light up that tells me the supply is in constant current mode, I know I probably have a short somewhere. This technique helps me keep the magic smoke in where it belongs.