Monergism.com gives the following definition:
Monergism: In regeneration, the Holy Spirit unites us to Christ independent of any cooperation from our unregenerated human nature. He quickens us through the outward call cast forth by the preaching of His Word, disarms our innate hostility, removes our blindness, illumines our mind, creates understanding, turns our heart of stone to a heart of flesh -- giving rise to a delight in His Word -- all that we might, with our renewed affections, willingly & gladly embrace Christ. The Prophet Ezekiel inspired by the Holy Spirit asserted "I will give them an undivided heart and put a new spirit in them; I will remove from them their heart of stone and give them a heart of flesh. Then they will follow my decrees and be careful to keep my laws. They will be my people, and I will be their God." (Eze 11:19, also 36:26) The Apostle Paul said, "For we know, brothers loved by God, that he has chosen you, because our gospel came to you not only in word, but also in power and in the Holy Spirit and with full conviction." (1 Thess 1, 4, 5). I.e. In regeneration the word does not work alone but must be accompanied by the "germination" of the Holy Spirit. And again "...you have been born again, not of perishable seed but of imperishable, through the living and abiding word of God." (1 Pet 1:23)
The Century Dictionary defines it as follows:
"In theology, the doctrine that the Holy Spirit is the only efficient agent in regeneration - that the human will possesses no inclination to holiness until regenerated, and therefore cannot cooperate in regeneration."
It means that the very desire for faith, by which we believe in Him who justifies the ungodly comes to us through regeneration -- and if anyone says that this belongs to us by nature and not by a gift of grace, that is, by the inspiration of the Holy Spirit amending our will and turning it from unbelief to faith and from godlessness to godliness, he/she ignores the teaching of the Apostles, for Paul says, "...Even when we were dead in sins, [God] hath quickened us together with Christ, by grace ye are saved." and "...he saved us, not because of works done by us in righteousness, but according to his own mercy, by the washing of regeneration and renewal of the Holy Spirit." (Titus 3:5) And again, "For by grace you have been saved through faith; and this is not your own doing, it is the gift of God" (Eph. 2:8). or if anyone makes the assistance of grace depend on the humility or obedience of man and does not agree that it is a gift of grace itself that we are obedient and humble, he contradicts the Apostle who says, "What have you that you did not receive?" (1 Cor. 4:7), and, "But by the grace of God I am what I am" (1 Cor. 15:10).
It is in contrast to synergism which the Century Dictionary defines as
"...the doctrine that there are two efficient agents in regeneration, namely the human will and the divine Spirit, which, in the strict sense of the term, cooperate. This theory accordingly holds that the soul has not lost in the fall all inclination toward holiness, nor all power to seek for it under the influence of ordinary motives."
They also offer a more indepth treatment here.