I have seen Noah's Ark listed one of the "types" in Scripture -- something that occurred, but that also foreshadowed something else that would come later.
What exactly, then, does the story of Noah's Ark foreshadow?
The flood is explicitly used typologically twice in the New Testament.
Jesus, speaking of the final judgment (Matthew 24:37-41), says it will be like "the days of Noah".
1 Peter 3:20b-22 says that the flood prefigured the sacrament of baptism.
Over the centuries Christians have found additional typology in this story:
This is only a sample; you can find longer lists here and here. Some of the connections are more explicit in the King James Bible; newer translations use different phrases that don't always match up, but the similarity should still be apparent.
Traditionally, many Christian theologians have likened the flood story to that of Christ's coming and sacrifice.
Basically, all of Mankind was doomed by the flood, but God, the Redeemer, found a way to save. One was found righteous, Noah, so God commanded him to build the ark to save mankind.
We are doomed to die because of sin. That is the flood. God, sent Jesus to redeem us; to save us from calamity. God's judgement came down on Christ just as it came down on the wicked of Noah's time. Just as there was only one Ark there is only one Jesus by which we can be saved. Noah and his family were spared by the Ark just as the church is spared by Christ.
The 'types' you are referring to is the theology that the Old Testament is filled with stories that show a 'type' of Christ that gives a kind of Gospel story in a sort of allegory. It is sometimes called typology.
I coincidentally read this summary from this page on an unrelated subject yesterday. I like the wording.