Electric lamp and City electricity frequency As far as I know the Public Power Supply frequency is 50hz.
Does it mean that lamps get on and off constantly?
Or they just remain on?
When you have some thing rotating it seems that light is not continuous as in certain speeds of rotation it looks backward or stopped.
If they do actually turn on and off. Why do we see only bright time not the dark (maybe i should ask biology part)
 A: The flow of electrons is oscillating (=alternating current): the current at time $t$ is $I(t)=I_0 \sin(\omega t)$. Electric power (the energy of the flow) is $P(t)=I(t)V(t)$, and for a resistive circuit (using Ohm's law) it is $P(t)=I^2(t)R$ where $R$ is the resistance. So the power is $P(t)=I_0^2 R  \sin^2(\omega t)$ - which is indeed varying between zero and some finite value. Were lamps to just shine proportional to their power they would be flickering at 100 Hz. 
In reality lamps respond more slowly to the current. An incandescent filament is heated until it glows, and the time constant of fading is relatively long (say 0.1 seconds) so the variable heating merely leads to a very small amount of flicker since even during the "off" moments every 1/100 second it only has time to decay by a few percent. The thicker the filament the more heat it can store, the slower it responds, and hence it flickers less [1]. This can still be annoying since the eye tries to track the varying light [2], but above the 50-90 Hz normal human flicker fusion frequency where we cannot detect the changes it is not noticeable [3].
However, fluorescent bulbs respond more rapidly and can hence have large oscillations in light output. This is why some get tired by fluorescent light [3]. LEDs are also very quick: when the eye does a fast saccade movement across a display it is not uncommon to notice a flickering as a spatial pattern. This may be especially noticeable for sharp edges, where it might be possible to notice even 500 Hz [4]. 
[1] Forsythe, W. E., Easley, M. A., & Hinman, D. D. (1938). Time constants of incandescent lamps. Journal of Applied Physics, 9(3), 209-214. http://aip.scitation.org/doi/abs/10.1063/1.1710410
[2] Emanuel, A. E., & Peretto, L. (2004). A simple lamp-eye-brain model for flicker observations. IEEE transactions on power delivery, 19(3), 1308-1313.
[3] https://en.wikipedia.org/wiki/Flicker_fusion_threshold
[4] Davis, J., Hsieh, Y. H., & Lee, H. C. (2015). Humans perceive flicker artifacts at 500 Hz. Scientific reports, 5. https://www.nature.com/articles/srep07861
