Question

What is the meaning and the significance of the phrase double translation

Answer 1

Double translation is when  for example:

Someone translates Spanish into Chinese.
then they would translate the Chinese back into Spanish
The translation of Spanish has to be as close to the exact words used in the first document.

hope this helps

so for example: 

I like bananas (english)
私はバナナが好き (japanese)
then in like 1 min later....
私はバナナが好き translate back to "I like bananas"

hope this helps

Answer 2

It's like saying spanish and english