After Adam and Eve sinned, their eyes were opened and they realized their nakedness, so they sewed fig leaves together to cover themselves and hid from God. Their own covering could not deal with their shame or restore their standing before Him; only God’s provision could do that.
The sermon draws out the pattern this sets for the rest of Scripture: sin brings a shame we cannot cover on our own, and it is God who provides an acceptable covering. What Adam and Eve could not accomplish with fig leaves, God accomplishes through the atoning provision that ultimately points forward to Christ.