Simply put, monergism is work that is done by one agent, while synergism is work that is done by two agents. If you are a Christian you’ve probably heard of, and perhaps thought about sanctification. Sanctification is the effect of being set apart by God, for God. In this process, He progressively conforms your will and behavior to His. He does this work by the power of His Holy Spirit, who indwells the believer. As an effect of this conforming work, the believer thinks and behaves differently than he did before God worked in him.
I think part of the problem with this question is that people associate monergism with Calvinism. Calvinists believe justification to be completely monergistic. So when a Calvinist starts talking about sanctification tons of people just stop listening. You might be surprised to know that many Calvinists think sanctification is synergistic.
Having said that, I think if we consider where sanctification finds its origins we can be helped. Think about the Bible for a moment. It was written by God. No Christians doubt this. We know that He wrote it by using individual men. These men had their own lives, with their own personalities, and experiences. They made real choices and lived the consequences. We also know that they wrote exactly what God wanted them to. We also know that unless God determined for them to have the experiences, and lives that they had, we wouldn’t have the same Bible.
We wouldn’t say that a pencil was synergistically responsible for a written work because it is not at all an agent equal to the author. The literature did not find its origins in the pencil but in the mind of the author. We would say that the author monergistically created the work of literature. The problem is that our man-centered theology and thought process gets in the way of seeing how sanctification is no different. Of course, we are used in the process of sanctification and it is being worked out on us and in us, thanks be to God. His glory should be the primary focus of our lives because God is perfectly glorious. We can’t equate ourselves with God. When we elevate our stature and lower God’s, is when we assume synergism. We are simply His creatures, part of His creation, that has sprung from His mind, that He is using to bring glory to Himself, which is the most loving thing He could do for us and to us.
So much like a baby in a crib, given that all things it needs are provided by God, it will grow according to the plan that God has laid out for it. No force of its will can make it grow faster or slower. Sanctification is like that process. We are growing in faith, holiness, and knowledge of our own personal sin. We are producing works in keeping with the Spirit. Let’s not equate ourselves in err to God. We are made in His image, but nonetheless, we are made.