In the Bible, generally the types are in the Old Testament and the antitypes are in the New Testament; that is, many Old Testament events and practices foreshadow certain events and practices in the New Testament. Let's consider an example for clarification purposes.
I Peter 3:18-22 reads - "For Christ also suffered once for sins, the just for the unjust, that He might bring us to God, being put to death in the flesh but made alive by the Spirit, by whom also He went and preached to the spirits in prison, who formerly were disobedient, when once the Divine longsuffering waited in the days of Noah, while the ark was being prepared, in which a few, that is, eight souls, were saved through water. There is also an antitype which now saves us-baptism (not the removal of the filth of the flesh, but the answer of a good conscience toward God) through the resurrection of Jesus Christ, who has gone into heaven and is at the right hand of God, angels and authorities and powers having been made subject to Him."
This is a difficult text and worthy of a thorough analysis. However, at this time we want to focus on what we can learn from it about types and antitypes. In the future, Lord willing, we will revisit it for an in-depth study.
According to I Peter 3:20,21, baptism is an antitype, and the flood of Noah's day was the type or shadow. Think about how these two things correspond. The waters of the flood lifted up the ark and delivered Noah and his family (obedient believers) from the destruction of the old world (Gen. 6-8). Today, the waters of baptism deliver obedient believers from the destruction of eternal condemnation--by washing away sin (cf. Acts 22:16). The floodwaters separated those who were saved from those who perished. Today, baptism separates those who are saved from those who are lost. The flood destroyed the evils of the old world and enabled Noah and his family to emerge into a new existence. Today, baptism washes away one's sins and enables that person to begin a new life for God (cf. Rom. 6:4).
Truly, the global flood and baptism of the Great Commission (cf. Matt. 28:19,20) correspond on many points. The flood was the type or shadow, and baptism is the antitype or substance. It was no accident that the flood and baptism have so much in common--God planned it that way. He planned for the flood to prefigure or foreshadow baptism. Of course, Noah didn't have any idea that being saved through the flood waters was foreshadowing salvation through baptism today, but we can see the resemblance and such is confirmed explicitly in I Peter 3:21.
Now that we have introduced the concept of types and antitypes, tomorrow, in our feature lesson, we will consider an extensive relationship of such concerning the Passover and Jesus Christ.