Basically, Newton's ideas matched up better with experiments and observations about the natural world than Aristotle's did. Newton gave a rigorous mathematical framework that made very specific predictions about our world, while Aristotle in general made more comparative laws, that even when true were less useful than the certainty Newton's laws gave us. Many of Newton's laws have been found to be at least partially incorrect now, for instance his laws of motion fall apart at speed nearing the speed of light, his laws of gravity fall apart when talking about more than two objects and in the presence of large gravitational fields that are close together, and Newton's law of cooling is just untrue in general (though can make some approximations in narrow temperature ranges).
