This is the word appearing in Titus 3:5, where we read, "He saved us, not on the basis of deeds which we have done in righteousness, but according to His mercy, by the washing of regeneration and renewing by the Holy Spirit" (NAS). Regeneration, or rebirth (NIV) appears in connection with "washing." Through the Spirit one is renewed.
Note the very close parallel to John 3:5 (conveniently having the same chapter and verse numbers), where we are born of water but also born of Spirit, just as we are baptized by water and Spirit.
Palin is the Greek word for again, genesia the word for birth or generation. Placed together, the nu of palin drops out, as two medial gammas are pronounced "ng-".