I'll start by hazarding a technical Bergerian definition:
Pre-evangelism is the means by which Christians attempt to set up the plausibility structures that make possible the reception of Christian gospel and its concomitant worldview.
Okay... less technically so...
Pre-evangelism is considered to be an activity that a Christian engages in with the non-Christian, whereby he or she tries to make the non-Christian more open or receptive to giving the Gospel a hearing. Pre-evangelism may or may not lead to a discussion of the Gospel. Evangelism on the other hand is the actual presentation of the Gospel to a non-Christian. Which activity is pursued first is dependent upon the situation that one finds themselves in.
At the very least, the goal of Pre-evangelism as with Evangelism is not simply to gain converts and then drop them, but it is to impact people in such a way that there is benefit to the lives that they live through and through. It is to help people with various struggles (existential, financial, sickness, etc.) in life, enter into those struggles with the crucified God and show them how Jesus Christ helps them get through those difficult times. There is more that can be said but . . .
Meekness and Truth Ministries - David Geisler (Yes. Indeedy. The son of Dr. Norman Geisler.) - Basically about Pre-Evangelism
Pre-Evangelism - short article by Dr. Bruce M. Bumgardner
Evangelical Apologetics by Alister McGrath ~ In this article Dr. McGrath suggests that Apologetics is a form of Pre-Evangelism.
R.C. Sproul Lecture's on Pre-Evangelism & Post-Evangelism can be purchased at Ligonier.
"Dr. Sproul, explains that, even though only the Holy Spirit can change a person’s heart and mind (bring them to repentance), we see the very important dimension of apologetics in what he calls “pre-evangelism” and also what we call “post-evangelism”."
"What, after all, is Apollos? And what is Paul? Only servants, through whom you came to believe—as the Lord has assigned to each his task. I planted the seed, Apollos watered it, but God has been making it grow. So neither the one who plants nor the one who waters is anything, but only God, who makes things grow."
~ 1 Cor. 3:5-7