What does Baptism properly signify?

From St. Charles-Marie De Veil's (1630-1686) "A Literal Explanation of the Acts of the Holy Apostles"

Lastly, There is another thing that evinces the necessity of plunging the parties to be baptiz'd, for that St. Peter asserts, the Genuine end of Baptism, was not to represent the inward washing away from sin; which may be represented by any exteriour washing of the body; but to express the Death and Resurrection of Christ, as also our own, and our belief of both Resurrections, as the most famous Sir Norton Knatchbul in his learned Notes printed at Oxford, anno Dom. 1677. with the licence of the Vice-chancellour, observes upon that place of Peter, whose words tho long, I cannot but transcribe, they are so full of truth and weight.

The sense and meaning of Peter is, saith he, That Baptism which now saves us by Water, that is, by the assistance of Water, and is Antitypical to the Ark of Noah, does not signify the laying down of the filth of the Flesh in the Water, but the covenant of a good Conscience toward God, while we are plung'd in the Water, which is the true use of Water in Baptism, thereby to testify our belief in the Resurrection of Jesus Christ; so that there is a manifest Antithesis between these words By Water, and, by the Resurrection, nor is the Elegancy of it displeasing. As if he should say, The Ark of Noah, not the Flood, was the Type of Baptism, and Baptism was an Antitype of the Ark, not as Baptism is a washing away of the filth of the Flesh by Water, wherein it answers not at all to the Ark; but as it is the Covenant of a good Conscience toward God by the Resurrection of Christ, in the belief of which Resurrection we are sav'd, as they were sav'd in the Ark of Noah. For the Ark and Baptism were both a Type and Figure of the Resurrection, so that the proper end of Baptism ought not to be understood as if it were a Sign of the washing away of sin, altho it be thus oftentimes taken metonymically in the New Testament, and by the Fathers, but a particular signal of the Resurrection by faith in the Resurrection of Christ. Of which Baptism is a Lively and Emphatical Figure, as also was the Ark out of which Noah returned forth as from the Sepulcher to a new life, and therefore not unaptly called by Philo, The Captain of the New Creation. And then the Whales belly out of which Jonas after a burial of three days was set at liberty: And the Cloud and the Red-sea in which the people of Israel are said to have been baptiz'd; that is, not washed, but buried; for they were all Types of the same thing as Baptism, not of the washing away of sin, but of the Death and Resurrection of Christ, and our own. To which truth the Apostles, the Fathers, the Scholasticks, and all Interpreters agree. The thing is so apparent as not to need any Testimonies; but because there are not a few, who do not vulgarly teach this Doctrine, it will not be superfluous, to produce some of those innumerable testimonies that I may not seem to speak without book

- St. Charles-Marie De Veil, A Literal Explanation of the Acts of the Holy Apostles, commentary on Acts 2:38.