Peter makes a plain statement that it is not the physical water which has the saving effect (“not the removal of the filth of the flesh”). Salvation is accomplished by the resurrection of Jesus and our union with Him.
Wilson, like many, takes this verse to mean something along the lines of "Baptism now saves you, not the water part that removes dirt, but what the rite represents, which is a clean conscience before God."
However, "dirt" is not the best translation of "rhupos" which means "moral or ceremonial impurity" (James 1:21; only other NT place it appears, but MANY times in the LXX). Thus this verse is a close corollary of the argument of Hebrews 9-10 (which discusses baptisms as well; Heb 9:10; 10:22). The washing (baptismos) doesn't save by washing away the flesh's "ceremonial uncleanness" (rhupos), functioning as it did in the Old Covenant, but by washing the conscience (Heb 9:9, 13-14).
