The following is an excerpt from Dr. Thomas Holland's Crowned With Glory, ©2000, used with permission.
Acts 12:4 - "after Easter"
"And when he had apprehended him, he put him in prison, and delivered him to four quaternions of soldiers to keep him; intending after Easter to bring him forth to the people."
The Greek word pascha is translated as Passover in the KJV with this one exception where it is translated as Easter. Therefore, some point to this passage as a translation error on the KJV's part. However, earlier English translations such as Tyndale's NT, the Great Bible, and the Bishop's Bible also translated pascha as Easter in this verse, showing that the understanding here dealt with something other than the Jewish Passover. Also, the translation of pascha as Passover in Acts 12:4 was known to the king's translators since this is the reading of the Geneva Bible.
The use of the word pascha in early Christian writings dealt with the celebration of Easter, and not just the Jewish Passover.  Dr. G. W. H. Lampe has correctly stated that pascha came to mean Easter in the early Church. The ancient Christians did not keep the Jewish Passover. Instead they kept as holy a day to celebrate the resurrection of Christ near the time of both Passover and the pagan festival celebrating the goddess Ostara. Dr. Lampe lists several rules and observances by Christians in celebration of their pascha or Easter. Lampe also points to various Greek words such as paschazo and paschalua that came to mean celebrate Easter and Eastertide.  Likewise, Dr. Gerhard Kittel notes that pascha came to be called Easter in the celebration of the resurrection within the primitive Church. 
It should be noted that the English word Easter originally carried a meaning that would encompass the Jewish Passover. The Oxford English Dictionary states that Easter also means, "The Jewish passover" and cites examples dating to 971 A.D. Likewise, the Coverdale Bible often used the word Easter instead of Passover in its translation because the two had the same meaning to the English mind. Further, the Homilies of the Church of England (1563) refers to "Easter, a great, and solemn feast among the Jewes."  Therefore, we see by definition, that the word Easter is correct in the understanding of the English language.
There is also a connection between the Christian Easter as we have it and the pagan celebration of Ostara. Early Christians in Rome could not openly celebrate the resurrection of Christ, so they held their celebration at the same time as the pagans. Dr. William C. Martin writes:
Modern observance of Easter represents a convergence of three traditions: (1) The Hebrew Passover, celebrated during Nisan, the first month of the Hebrew lunar calendar; (2) The Christian commemoration of the crucifixion and resurrection of Jesus, which took place at the feast of the Passover; and (3) the Norse Ostara or Eostra (from which the name "Easter" is derived), a pagan festival of spring which fell at the vernal equinox, March 21. Prominent symbols in this celebration of the resurrection of nature after the winter were rabbits, signifying fecundity, and eggs, colored like the ray of the returning sun and the northern lights, or aurora borealis. 
It seems that pascha can mean more than the Jewish holy day of Passover. In fact, Greeks today who wish to send the greeting Happy Easter say, kalee pascha. Literally it means good Passover. However it has come to mean good or happy Easter.
Additionally, there is a possible problem if we understand this verse to mean the Jewish Passover. Verse three of this chapter states that Peter was taken during, "the days of unleavened bread." The next verse then speaks of Easter in the KJV. If the word is translated as Passover, we have the Days of Unleavened Bread coming before the Passover. In the Biblical use of the term, Passover came before the Days of Unleavened Bread (Exodus 12:1-8, 15, 19; 13:7; Leviticus 2:11; and Deuteronomy 16:4). Contextually, it would seem that this pascha that followed the Days of Unleavened Bread was not the pascha that preceded the capture of Peter. Instead, it is likely to refer to the Roman celebration of Ostara, hence called Easter.
 See Dr. Walter Bauer's, A Greek-English Lexicon Of The New Testament And Other Early Christian Literature (Chicago: The University of Chicago Press, 1957), 633.
 G. W. H. Lampe, A Patristic Greek Lexicon (Oxford: Clarendon Press, 1961), 1048-1049.
 Gerhard Kittle, Theological Dictionary Of The New Testament, Vol. II. (Grand Rapids: Eerdmans, 1965), 901-904.
 Oxford English Dictionary, 492.
 William C. Martin, The Layman's Bible Encyclopedia (Nashville: The Southwestern Company, 1964), 204.