At the heart of this is another bloke's name, Ohm,and his law. This states at its simplest that, "One Volt will push one Amp through one Ohm."
The volt can be considered as pressure. It is the potential difference between the positive and negative at any instant, although no power need be flowing. The battery in your radio is, say, 6 Volts, and remains so even with the radio switched off. (Let's not get involved here with internal resistance of batteries)
That's all fine and dandy until you let the electricity flow through something (a resistance, measured in Ohms). The amount of electricity that goes through that something to do some work (light heat motion or combination of etc.) is measured in Amperes.
With these three elements it is possible to calculate what will happen in any closed loop. If the resistance remains constant, increasing the Voltage will increase the current proportionately. If the Voltage stays the same and the resistance changes then the current in Amps changes in inverse proportion to the resistance in Ohms. (Say, 1 Amp with 100 Ohms, then at 50 Ohms, that is half the resistance, then the Amps passing would be doubled to 2 Amps).
Watts are units of power, used to compare consumption of electricity under varying conditions. Watts are Volts times Amps. 100 Watts could be 50 Volts pushing 2 Amps through 25 Ohms or equally 250 Volts pushing 0.4 Amp through 625 Ohms.
To really get to grips with this, I recommend you study Ohm's Law and see that what it has to say is applicable to loads of things, not just electricity!