Thomas Boston, the Scottish Puritan, gives the best treatment on Effectual Calling I have read. He starts with a brief explanation of what it is:
Effectual calling is the first entrance of a soul into the state of grace, the first step by which God’s eternal purpose of love descends unto sinners, and we again ascend towards the glory to which we are chosen. And upon the matter, it is the same with conversion and regeneration.
Next he shows what it is not, Negatively, then what it is, Positively.
Negatively
It is neither the piety, parts, nor seriousness of those who are employed to carry the gospel-call to sinners, 1 Cor. iii.7. Indeed, if moral suasion were sufficient to bring sinners back to God, men that have the art of persuading, and can speak movingly and seriously could not fail to have vast numbers of converts. But that
work is not so brought about, Luke xvi. ult. Hence said Abraham to the rich man in hell, ‘If they hear not Moses and the prophets, neither will they be persuaded though one rose from the dead.’ Never did these, conjunctly or severally, appear in any, as in any, as in Christ, who ‘spake as never man spake.’ But behold the issue, John xii. 37, 38. ‘But though he had done so many miracles before them, yet they believed not on him: that the saying Esaias the prophet might be fulfilled, which he spake, ‘Lord, who hath believed our report? and to whom hath the arm of the Lord been revealed?’
Neither is it one that uses his own free-will better than another does, Rom. ix. 6. ‘It is not of him that willeth, nor of him that runneth, but of God that sheweth mercy.’ For every man will be unwilling till the power from another quarter make him willing, John vi. 44. If it were so, one man should make himself to differ from another in that grand point. But hear what the Apostle Paul says, 1 Cor. iv. 7. ‘Who maketh thee to differ from another?’ Men are dead in trespasses and sins, and such cannot difference themselves.
Positively
We may say in this case, ‘Not by might, nor by power, but by the Spirit of the Lord.’ It is the Spirit of the Lord, accompanying the call of the word, that makes it effectual, John vi. 63. Hence days of the plentiful effusion of the Spirit are good days for the take of souls, and contrarywise, when the Spirit is restrained, Psal. cx. 3. Therefore Isaiah resolves the question thus, ‘Who hath believed our report? and to whom is the arm of the Lord revealed?’ The report may reach the ears, but it is the arm of the Lord that must open the heart…..
-from A Complete Body of Divinity by Thomas Boston, Volume 1
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