It is the sympathetic vibration, the principle of like attracts like, that forms this bond as we sing with other people and create harmonious vibrations with our voices. The joining of the sounds heralds the joining of the spirit.
I have sung sacred chants in a number of different languages and there is a difference between singing them in the original language or English. You will find the same thing if you were to sing Indian chants in Sanskrit or Gregorian chants in Latin and then see how they feel translated into English. A totally different feel.
There is a certain musicality in the way each song or chant is composed. When a person is putting words or phrases together, they have a sense of what flows together. For example, there are different words that mean the same thing, and each certainly has a different feeling sung. A native speaker has a feel for what word will fit into a phrase smoothly and melodically.
Rumi's poetry became popular in the US and got a larger audience in many countries because of Coleman Barks' new interpretations of them for a similar reason. Coleman will emphasize to you that he is not a translator. As an interpreter, he took the English translations from someone who was a translator and then found the English phrases that seemed to fit the meaning best.
A great way to get some experience of what it is like is to sing sacred chants in different languages is by participating in the Dances of Universal Peace, which I used to participate in a lot.