The second is defined as the duration of 9,192,631,770 cycles of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom. So what is meant by a cycle of radiation?

• A complete cycle of the sine wave. – PM 2Ring May 29 at 15:45
• But won't any radiation of same frequency as that emitted due to the transition between the two hyperfine levels of the ground state of the cesium-133 atom take the same time? – bo habib Jun 4 at 9:44
• Yes, by the definition of frequency. What EM source do you have in mind that has exactly the same frequency? ;) Note that the caesium atoms should be at 0K to produce the desired frequency, so a practical caesium clock has to make a compromise. – PM 2Ring Jun 4 at 9:58
• – PM 2Ring Jun 4 at 10:07

Taken a point in the space, hit by the radiation, the electric field in that point will oscillate periodically, as $$\sin(\omega t)$$ (where $$t$$ is the time). The oscillation will repeat exactly equally after a period $$T=2\pi /\omega$$.
The part of oscillation taking place during a time interval of length $$T$$ is "one cycle". It is, for example, the part of oscillation between two minima (or between two maxima).
A second is defined as the time needed to perform 9,192,631,770 cycles, i.e. 1 s=9,192,631,770 $$T$$.