PWM provoques a lot of discussion. Part of the time answers are clear, part of the time they are not. This, by itself is a PWM. I would say the duty cycle of the answers is the period between people answering and you getting more confused.
But, your question was duty cycle.
Duty cycle is the amount of "ON" or "OFF" inside a PWM frequency that would affect a load. Still confused? Let me try to explain using analog:
Imagine a 2V lamp connected to a 2V battery. It is connected directly. If you let go one of the wires that's connected to the battery, the lamp will go out, as expected. Now, imagine the same experience and you are kind of a superhero with supervision powers and a superfast fingers to manipulate a stopwatch and the battery wire connected to the lamp.
With your right hand holding the stopwatch (you are a right handed superhero) and the left hand holding the wire, you connect the wire and at the exactly same time you start the stopwatch. With your superhero precision vision, you can precisely determine when the bulb reaches its plenitude of brightness and stop the stopwatch.
You look at the stopwatch with your ultra-high-precision vision and it reads 50ms.
It took the lamp to go from complete darkness to full brightness in 50ms. You imagine, with your superhero imagination that it might take the same amount of time to go from full brightness to complete darkness in the same amount of time.
So, you reset your stopwatch, and pull the wire away from the battery and watch the light diminish until it's gone. You stop the stopwatch and it reads, with no coincidence, 50ms.
So, you analyze the data you have and discover that you need, at least, 50ms to turn the lamp on and another 50ms to turn the lamp off. You need one 100ms cycle (word cycle here is important) to manipulate the lamp completely. But, but, and one more but, you need 50ms to make something happen. You need 50ms to turn it on, and you need another 50ms to turn it off. But, another but, it was already in one state, and it took you 50ms to reach the exact other end of your initial state.
So your PWM period will be 50ms or 20Hz.
So, (so much so's) if you want to develop a gadget that will turn on the lamp with half of it's brightness, you would use a 50% duty cycle.
The exact math for this is using integrals. And it's easy for a superhero...
For a real world example, I like doing slot car racing. A slot car usually has a 12V DC motor. I think you may have tried this experiment at home, when you got a 9V battery and a variable resistor and tried speeding up the motor?
If you don't, I will try to illustrate what happens, using a 9V battery, a variable resistor and a 9V motor.
When you apply 9V thru a variable resistor, the motor will get variable voltage (right to say would be variable current, but let's pretend we don't understand that far). So, you start your experiment, having a voltage meter at the motor wires, and see that you got 1V and the motor doesn't do anything (using your superhero temperature detection, you see it is getting slightly warm, even for a superhero to detect). You turn the variable resistor to 2V and the motor doesn't start spinning, but, but, and another but, you start hearing and feeling a "hummmmm" from the motor (you are holding the motor between your fingers). You keep on turning up the variable resistor. When you get 2.75V, the motor starts spinning. But you see that it started spinning at 100rpm instead of 1rpm. Why is this?
It's because of something called slip, but this is not the point. Our point is PWM and how to start spinning a motor at 1rpm.
We said that the motor is powered by 9V. It was constructed and engineered for 9V. To get full rotation, you need to apply 9V. So what if I apply 9V to the motor, for a period that is so short (duty cycle), and repeat this at regular intervals (PWM frequency)?
The engine will receive all the power it needs for that period you determined and will react at it.
You'll see that it will spin very slowly. This is a real example and easy to do at home.
It's 3:30 am, woke up, got on the internet, and my wife is complaining that I'm typing. I think I'll go back to sleep. Hope it helped explaining.