Hyper-calvinism is just as harmful as legalism and as unbiblical as antinomianism. But what is hyper-calvinism? There’s more to it, but the New Dictionary of Theology gives a decent short answer to this question:
Hyper-calvinism is an exaggerated or imbalanced type of Reformed theology, associated with Strict and Particular Baptists of English origin and with Dutch-American Reformed groups. Originating in the 18th century before the Evangelical revival, it has always been the theology of a minority, which today is extremely small. Here are two definitions:
1. It is a system of theology framed to exalt the honour and glory of God and does so by acutely minimizing the moral and spiritual responsibility of sinners. It puts excessive emphasis on acts belonging to God’s immanent being (cf. Hidden and Revealed God)—the immanent acts of God—eternal justification, eternal adoption and the eternal covenant of grace. It makes no meaningful distinction between the secret and revealed will of God, thereby deducing the duty of sinners from the secret decrees of God. It emphasizes irresistible grace to such an extent that there appears to be no real need to evangelize; furthermore, Christ may be offered only to the elect (from P. Toon, The Emergence of Hyper-Calvinism in English Nonconformity, 1689–1765, London, 1967).
2. It is that school of supralapsarian ‘five-point’ Calvinism which so stresses the sovereignty of God by over-emphasizing the secret over the revealed will of God and eternity over time, that it minimizes the responsibility of sinners, notably with respect to the denial of the use of the word ‘offer’ in relation to the preaching of the gospel; thus it undermines the universal duty of sinners to believe savingly in the Lord Jesus with the assurance that Christ actually died for them; and it encourages introspection in the search to know whether or not one is elect (from the unpublished PhD thesis of C. D. Daniel, Hyper-Calvinism and John Gill, University of Edinburgh, 1983).