There have been a number of suggestions as to what exactly porneiva means. Four are most common.
1. Illicit incestuous marriages (Lev 18:6-18) – Witherington asserts that the word is used in this manner in 1 Cor 5:1 and perhaps Acts 15:20, 20, and 21:25. This is doubtful, especially in 1 Cor 5:1, where it seems more likely that an affair was in view rather than a marriage. The Acts 15 and 21 passages depend on a connection with Lev 16 which is tenuous at best. Isaksson says, “According to Jewish law, no divorce was necessary when a marriage involved an incestuous relationship of the first degree. In that case the marriage was regarded as a nullity” (Isaksson, p. 130). If Isaksson is right, and it seem reasonable that he is, then this exception would have no bearing for the Pharisees.
2. Premarital unchastity (cf Matt 1:19) – Geisler holds that it is premarital fornication (Geisler, p. 289: cf Deut 22:13-21). Isaksson also holds this view by arguing that “moiceiva and not porneiva was used to describe the wife’s adultery … Since it is a question of a married woman’s crime and her extra-marital sexual intercourse is described as porneiva, this word must mean a sexual offence committed by the wife before her marriage” (Isaksson, p. 135; contra BAGD, p. 693 [see above]). “The word porneiva should be understood as referring to the same kind of unchastity as that Joseph suspected Mary of, i.e. premarital unchastity” (Isaksson, p. 139). John Piper also hold this view connecting it specifically to the occasion of Mary and Joseph. He says, “Matthew includes the exception clause in particular to exonerate Joseph, but also in general to show that the kind of ‘divorce’ that one might pursue during a betrothal on account of fornication is not included in Jesus' absolute prohibition” (Piper, “Divorce and Remarriage”). John uses it in John 8:41 to describe the Pharisees’ view of the birth of Christ, of one of illegitimacy prior to marriage (i.e., premarital not extramarital) (See Piper, “Divorce and Remarriage”). However several objections should be made to this argument. The most common is that the Pharisees were inquiring about marriage, not betrothal. In this case, Piper’s assertion seems to lose some of its force. However, it is not insurmountable in view of the fact that the OT passage that addresses this very situation is Deuteronomy 22:13-21 where the couple is married when the premarital unchastity is discovered. Thus, a divorce would have been in order. The most solid argument against this view is that of Edgar who says that such a view “would place a higher value on faithfulness prior to marriage than on faithfulness once married” (House, p. 173).
3. Mixed marriage between a pagan and a believer – Isaksson says this question “had already been solved before Jesus’ time.” (Isaksson, p. 131). Furthermore it seems to have no specific place in the context.
4. Adultery or sexual unfaithfulness – This is the most common suggestion. The view that is suggested here is the view that porneiva is marital unfaithfulness (cf. NIV) including adultery but not limited to adultery as an act (it might include other sexual indiscretions short of adultery). Atkinson likens this to the rb*d* tw*ra#. The answer to this assertion by those who reject it is that there is a clear word for adultery (moiceiva) also used in the verse and the two (porneiva and moiceiva) are used in distinction is several passages in the gospels (Matt 15:19; Mark 7:21; Gal 5:19). “If he meant adultery in [chs.] 5 and 19 why did he not use the clear word?” (Ryrie, 1982, p. 186). Ryrie claims that the traditional Protestant view requires the equation of porneiva and moiceiva. Piper says, “the primary contextual evidence for Matthew's usage [ch. 15] is that he conceives of porneia as something different than adultery” (Piper, “Divorce and Remarriage”). Isaksson objects by saying, “We shall probably not find any pronouncement of a precise legal nature in which the wife’s extra-marital sexual intercourse is described as unchastity alone and not as adultery” (Isaksson, p. 132). However, the semantic range of the word is clearly within the bounds of “adultery.” BAGD asserts that porneiva is the word that connotes the “sexual unfaithfulness of a married woman” (BAGD, p. 693), thereby reserving moiceiva primarily for men. Blomberg says, “porn- root words were used much more commonly than moic- root words when female sexual infidelity was being described” (Blomberg, 178). Thus it is not unexpected for such a word to be used (cf. Feinberg, p. 329). Thus, the verse would read something like, “If a man divorces his wife except for adultery on her part, and marries another he commits adultery.”
Therefore, it seems that the most likely meaning of porneiva in this passage is adultery or sexual unfaithfulness to the marriage covenant.
I'll take Jesus! 
