I understand it to mean that happiness comes from just "being". When the voice inside our head is quiet, when we dont listen to the voices of others. It seems related to meditation.

Well, it's a Russian saying. Many times happiness in Russian romances (music style) or fairy tales compared with a bird or a butterfly. When it is close to you or you were so lucky to catch it, you are looking at this bird and afraid to breath, to not scared it and it will not fly away from you. So I guess here is the same meaning. Happiness loves silence and calm.

Thank you guys for your interesting comments. 
I just try to count how many years were "without war" or without  any fighting in the all world. And suddenly it can be only few hours, maybe...or nothing at all
Interesting. .if to think about the world in general. ..

Live with each other with no argues.