What role did Neoplatonism play in Augustine's conversion?

Neoplatonism played a vital role in St. Augustine's conversion to Christianity. As Augustine himself states quite explicitly in the Confessions, it was only when he came under the influence of the Neoplatonist Bishop Ambrose that he began to take Christianity seriously.
Since the time of St. Paul, Christian doctrine had become deeply imbued with certain elements of pagan philosophy. As Christianity spread throughout the Greek-speaking world, it needed to be able to speak to the educated using concepts they could readily understand. As time went on, Christian theology became almost a synthesis of Judaism and Greek philosophy, with a growing emphasis on the latter. St. Augustine was one of the many inheritors of this intellectual tradition.
As with many Christian Neoplatonists, however, Augustine came to see Greek philosophy as a means to an end, as a way of clarifying certain elements of Christian dogma and doctrine. For instance, Augustine draws freely—perhaps a little too freely—upon Plotinus's elaborate metaphysical system to provide what he considers to be compelling proof of the veracity of the Trinity—the Father, the Son, and the Holy Spirit. Whether Augustine's somewhat liberal interpretation of Neoplatonism is entirely accurate—and one would argue that it is not—there's no doubting his sincerity in believing that the Bible and the Neoplatonists said exactly the same thing in relation to key elements of Christian doctrine such as the Trinity.
As an educated man with a generous stock of pagan learning, Augustine naturally gravitated towards the Neoplatonist school of philosophy for intellectual sustenance. But in this elaborate system of thought, he found much more; he found that Neoplatonist metaphysics could provide an entrée into learned, academic circles for a religion hitherto regarded as a vulgar collection of superstitions fit only for women and slaves. Neoplatonism allowed Christianity to be taken seriously, not just by Augustine himself, but countless others who came after him.