Monergism

At the heart of the Reformation was one of the most fundamental questions of the Christian faith: How can I be saved from eternal damnation? The answer of all the leading Reformers was one and the same: only by God's free and sovereign grace. As J. I. Packer and O. Raymond Johnston have pointed out, it is wrong to suppose that the doctrine of Justification by faith alone, that storm center of the Reformation, was the crucial question in the minds of such theologians as Martin Luther, Ulrich Zwingli, Martin Bucer, and John Calvin. This doctrine was important to the Reformers because it helped to express and to safeguard their answer to another, more vital, question, namely, whether sinners are wholly helpless in their sin, and whether God is to be thought of as saving them by free, unconditional, invincible grace, not only justifying them for Christ's sake when they come to faith, but also raising them from the death of sin by His quickening Spirit in order to bring them to faith.
Michael A. G. Haykin

Synergism is "...the [erroneous] 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."To put it simply, synergism is the belief that faith is produced by our unregenerated human nature.

"I say that man, before he is renewed into the new creation of the Spirit's kingdom, does and endeavours nothing to prepare himself for that new creation and kingdom, and when he is re-created has does and endeavors nothing towards his perseverance in that kingdom; but the Spirit alone works both blessings in us, regenerating us, and preserving us when regenerate, without ourselves..."
Martin Luther Bondage of the Will, pg. 268

Faith in the living God and his Son Jesus Christ is always the result of the new birth, and can never exist except in the regenerate. Whoever has faith is a saved man.
C.H. Spurgeon from Faith and Regeneration