I found out it was volume setting problem, that could be changed in "Audio MIDI setup"
Plug in the headphones (if there is problem with headphones - if problem exists when using internal speakers, don't plug headphones)
Find in Spotlight "Audio MIDI setup" app:
And open app :
Make sure that channel 1 and 2 have THE SAME volume set up. Set every channel to value "1" as here :
I have no idea how this disproportion in volume happened. But I would like to know. (I haven't tinker with volume before - except simple volume up/down via headphone control or keyboard's function keys)
This answer is based on the "The Hefster's" answer from :
(I post screenshot because https://discussions.apple.com doesn't support linking to stand alone posts)