What does 天將降大任於斯人也,必先苦其心志 mean?
You can find James Legge's translation on ctext. Here's the snippet:


  故天將降大任於是人也，必先苦其心志
  when Heaven is about to confer a great office on any man, it first exercises his mind with suffering


You can also take a look at A. Charles Muller's translation of the same section:


  Thus, when Heaven is going to give a great responsibility to someone, it first makes his mind endure suffering. 


If you want to understand about the psyche behind such quotes you could flip through a book like The Oxford Handbook of Chinese Psychology which goes into some detail on their interpretation of the saying. One such excerpt notes:


  As stated in the Confucian doctrines, individuals should endure stress or suffering because these 'negative' experiences can be beneficial to individuals through strengthening their will, resilience, and inadequacies


Of course, you should consider the context around the quote, also, to get a clearer picture of what was being spoken of.