Answer:
The answer to the question: what does the phrase "hardened their hearts" imply, would be, that a situation or circumstance, made their emotions and feelings towards something, turn harder, and colder. Its like changing something that used to be soft, and maybe even gentle, into something hard, and harsh, and this happens usually when people are exposed to difficult, or constantly hard, circumstances, events, or even other people. The allusion to the word heart, always leads to the implication of feelings and emotions, while the allusion to the word "hardened" leads a listener to equate that to a rock, but mostly, to its tough characteristics. This is why the answer is that their emotions, or feelings, were turned harder, or colder, by the circumstances.