Kevin DeYoung gives a short summary of a book titled The Emergence of Hyper-Calvinism in English Non-conformity 1689-1765 written by Peter Toon; Kevin gives three lessons within the book. I'll give an excerpt focusing on the second lesson and then if you're interested, you can click on the link I'll provide to read the other two.
"2. Toon gives a solid definition of Hyper-Calvinism and it’s not the same as being really, really Reformed. In common parlance, Hyper-Calvinist simply means “I think you are too much of a Calvinist.” But that’s not a fair use of the term. Historically, Hyper-Calvinism has referred to a set of theological conclusions and practices, none of which mark any of today’s leading Calvinists.
Here’s Toon’s summary (with some paragraph breaks added):
[Hyper-Calvinism] was a system of theology, or a system of the doctrines of God, man and grace, which was framed to exalt and honour and glory of God and did so at the expense of minimising the moral and spiritual responsibility of sinners to God. It places excessive emphasis on the immanent acts of God–eternal justification, eternal adoption and the eternal covenant of grace. In practice, this meant that “Christ and Him crucified”, the central message of the apostles, was obscured.
It also often made no distinction between the secret and the revealed will of God, and tried to deduce the duty of men from what it taught concerning the secret, eternal decrees of God.
Excessive emphasis was also placed on the doctrine of irresistible grace with the tendency to state that an elect man is not only passive in regeneration but also in conversion as well. The absorbing interest in the eternal, immanent acts of God and in irresistible grace led to the notion that grace must only be offered to those for whom it was intended.
Finally, a valid assurance of salvation was seen as consisting in an inner feeling and conviction of being eternally elected by God. So Hyper-Calvinism led its adherents to hold that evangelism was not necessary and to place much emphasis on introspection in order to discover whether or not one was elect. (144-45)
So the main tenets include: little attention to message of the cross, no free offer of the gospel to call, no summons for men to be born again, a highly introspective doctrine of assurance, and collapse of the hidden and revealed will of God. This was Hyper-Calvinism, not simply being seriously Reformed."
For the other two points Kevin identifies click here.
R.C. Sproul gives a good, short explanation of Hyper-Calvinism in his commentary on Romans. I don't have the exact quote with me, but the main point he makes is that Hyper-Calvinists teach a symmetrical view of predestination, i.e., God decreed the elect's salvation from eternity, in time intervenes in their lives and creates saving faith in their hearts by grace. Those who aren't saved, God in time, intrudes into their lives and creates fresh evil in their souls (God causes sin) enuring their ultimate damnation. That is not orthodox reformed theology.