See G. R. Cragg, ed., The Cambridge Platonists (1968); E. Cassirer, The Platonic Renaissance in England (tr. 1953, repr. 1970).
The Cambridge Platonists were reacting to two pressures. On the one hand, the dogmatism of the Puritan divines, with their anti-rationalist demands, were, they felt, immoral and incorrect. They also felt that the Puritan/Calvinist insistence upon individual revelation left God uninvolved with the majority of mankind. At the same time, they were reacting against the materialist writings of René Descartes and Thomas Hobbes. They felt that the latter, while properly rationalist, were denying the idealistic nature of the universe. To the Cambridge Platonists, religion and reason were in harmony, and reality was comprised not of sensation, but of "intelligible forms" that exist behind perception. Universal, ideal forms (a la Plato) inform matter, and the senses are unreliable guides to reality.
As divines and in matters of polity, the Cambridge Platonists argued for moderation. They believed that reason is the proper judge of all disagreements, and so they advocated dialogue between the Puritans and the High Churchmen. They had a mystical understanding of reason, believing that reason is not merely the sense-making facility of the mind, but, instead, "the candle of the Lord" - an echo of the divine within the human soul and an imprint of God within man. Thus, they believed that reason could lead beyond the sensory, because it is semi-divine. Reason was, for them, of God, and thus capable of nearing God. Therefore, they believed that reason could allow for judging the private revelations of Puritan theology and the proper investigation of the rituals and liturgy of the Established Church. For this reason, they were called latitudinarians.