In many power supplies, there's CV & CC indicators. What does they mean?
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They are acronyms and stand for "Constant Voltage" or "Constant Current".
They usually are associated with a LED or an indicator of some kind, as you suggest. When you use a power supply you usually set the desired voltage and the maximum current. When you connect the load two things can happen:
In the first case the PSU become a current source: the current is limited to what you set and voltage drops accordingly, that's CC for you. In the second case what is costant is the voltage, so that's CV.
As an example, consider this case: you set the voltage at 10V and set the maximum current at 1A, then you hook up a load that is over \$10\Omega\$ . As you know that requires at most 1A, so the voltage is constant while the current can vary between 0A and 1A. If you then hook up a lower impedance load it would require a higher current, but now the current protection kicks in so the current is limited to 1A, and it is constant, while voltage varies between 10V and 0V.
"CV" stands for "constant voltage", and "CC" stands for "constant current". Most types of load need constant voltage to operate, so if the "CV" LED is lit, it means the PSU works fine with your load.
The PSU has a physical limit on how much current it can supply. If the load attempts to draw more, the PSU decreases the output voltage to keep the current consumed at its maximum, not beyond it. This mode is called "constant current". The PSU behaves as a current source, so that it changes its output voltage to keep its current constant.
Some types of rechargeable batteries require mixed mode charge, where the charge starts at constant current and finishes at constant voltage. Li-Ion ones are a good example. So the battery chargers designed for such batteries can have this kind of indication.