Contrast is identifying what is dissimilar between the Old and New Testaments on account of the discontinuity that Christ introduced by becoming a man. The Incarnation absolutely changes things. By becoming a man, Jesus forever altered reality and contrast is the act of identifying these differences. Jesus captured this very idea when he said that new wine requires new wine skins (Luke 5:37-38).
To preach contrast the preacher must be able to identify the differences between reality in the Old Testament and reality in the New Testament. He must also be able to explain why this shift has occurred on account of the Incarnation. For example, Leviticus clearly outlines the categories of holy, clean, and unclean. Leviticus also describes the many ways in which a person can move from one category to another. A person or thing is profaned (moves from holy to clean) and defiled (moves from clean to unclean) by coming into contact with someone or something that is in a lower category. On the other hand, a person or thing is purified (moves from unclean to clean) and sanctified (moves from clean to holy) by external time, water, shaving, and blood rituals. Movement from one category to another is caused by something external to the person or thing that is changing categories. By contrast Jesus teaches that nothing outside a person can make him unclean (Mark 7:14-23). The categories of holy, clean, and unclean remain, but movement from one category to another has changed. Now, a person is made unclean by what comes out of his heart. Therefore, all people are in effect unclean. No longer do simple external rituals purify and sanctify either. Now, the only way to be sanctified is by grace through faith in the ultimate purifying and sanctifying ritual, which is the crucifixion of Jesus. When a person receives grace through faith then the Holy Spirit circumcises the heart (i.e. the cutting off of sin) and He indwells that person, making him or her holy from the inside (though in an experiential sense sin remains a problem). There is, therefore, a major contrast between Levitical law and the Gospel. This difference is brought about by the Incarnation of Christ, who came not to save us externally but to save us from the inside-out.
Contrast enlightens us as to why reality seems different under the Old Covenant and the New Covenant. Although there remains great continuity between the Old and the New, the first coming of Christ altered reality forever.
 Greidanus, Preaching Christ from the Old Testament, 224.