What did Jesus mean by 'going for a second mile '? At Matthew 5:39-41 (NRSVCE) we read: 


  But I say to you, Do not resist an evildoer. But if anyone strikes you on the right cheek, turn the other also;   and if anyone wants to sue you and take your coat, give your cloak as well;   and if anyone forces you to go one mile, go also the second mile.


I wish to know about the backdrop against which a person could have been forced to go one mile, say by a soldier who was shifting his post and was looking for a native  to accompany him to his new place of posting. How do the Catholic teachings interpret the said  saying of Jesus?
This was a reference to a law by which the Roman could force a Jew to carry some goods for one mile and one mile only. Therefore, here Jesus meant that, if you just go one mile, there is nothing special, as that is the law. You must go further than that, by will and love. It might also have been an indication that the new covenant does not revolve on following the law, but in a new measure of love.

You can read it much better in this book, and the relevant quote below: