What does it mean that God does not impute trespasses to people?

It means that, before a lost person dies, God is not holding their trespasses against them. The Creator was in Christ reconciling the world to Himself. This non-imputation gives the unbeliever opportunity to believe the Gospel; but once that person dies, that opportunity is lost.

Les explains that Paul is telling us God was in Christ, reconciling the world back to Himself after He lost it in Adam, and not imputing their trespasses unto them. He says that means what it says: until that lost person dies and has lost his opportunity for believing the Gospel, his sins are not being held against him. Les also emphasizes that the One on the cross was the Creator, the same God of Genesis 1:1, who had to be God to taste death for every man and pay the sin debt of every human being.

2 Corinthians 5:19

To wit, that God was in Christ, reconciling the world unto himself, not imputing their trespasses unto them; and hath committed unto us the word of reconciliation.

What does it mean that God was not imputing the world's trespasses during the cross?

It means that at the cross God was not charging the world's offenses against them. Through Christ's death He was reconciling the whole alienated world to Himself, not counting their trespasses, and He has committed this word of reconciliation to His ambassadors.