One explanation might be the fact that the narratives played into well-established tropes about the Puritans' place in the New World. Surrounded by hostile peoples whose cultural practices the English found evil and savage, New Englanders, as they saw it, were tasked with creating an ideal society. In other words, it underscored their sense of divine mission in creating a "city on a hill," the establishment of which entailed the annihilation of area Indian peoples, including the Wampanoags who captured Rowlandson. This interpretation is one reason the book is still studied by modern scholars.
The book is also full of moral lessons, which is why ministers favored it. Under horrible circumstances, Rowlandson's faith allows her to survive, as she tells it. Indeed, she thanks God at various points in the narrative for using the horrors she experienced to chasten her and the people of Massachusetts. Another reason might be, simply, that it was full of graphic descriptions of what New Englanders viewed as horrible atrocities. Published in the wake of King Phillip's War, these images would have resonated with contemporary readers. Its popularity may be read as evidence of the degree to which it touched on deep-seated anxieties felt by New England colonists in what they still regarded as a hostile wilderness more than fifty years after initial settlement.