How is the flicker fusion rate interpreted as an on-off rate?
Short answer
A light flashing at 50 Hz means there are 50 flashes of light per second. The unit hertz means cycles per second. 1 cycle is the time it takes for the light to be ON and OFF. 50 Hz cycle time means a cycle time of 20 ms. If light ON and OFF times are equal, then the ON and OFF times are both 10 ms each.  

Background
The unit hertz (Hz) is a frequency unit in the International System of Units (SI) and is defined as


  one cycle per second


A textbook example where the unit Hz finds its use is a sine wave (Fig. 1). 1 cycle per second would be 1 Hz. A cycle, as can be seen in the figure, is a complete wave consisting of a positive phase followed by a negative phase. 

In the right panel of figure 1, a square wave is shown. Again, a cycle time is the time it takes for one complete square wave to develop, i.e. a positive phase and a negative one. 

 
Fig. 1. Sine wave (left) and square wave (right) sources: Simon Fraser University, Integrated Publishing

Now, in your example, you can depict the lights ON as the positive block in the square wave in Fig. 1 above, and the lights OFF as the negative phase. Together (light ON + OFF phases) they form one cycle. So a light pulsing at 50 Hz means it flashes ON and OFF 50 times.

The cycle time then is 1 second/50 = 20 ms. If we assume that the ON and OFF times are equal, which they obviously do not have to be, then light ON is 10 ms, lights OFF is 10 ms. 

On the wikipedia page on the hertz unit, a flashing light example is actually illustrated and explained.