An anti-Pope is someone who appears to have a claim to the Office of the Papacy, but the claim is not clearly established or accepted.
There have been many anti-Popes. One anti-Pope (namely Hippolytus of Rome) is actually a Saint of the Church. So being an anti-Pope is not the same as being an anti-Christ. Most anti-Popes were godly men who believed they were acting in accordance with God’s will.
A person becomes Pope by virtue of being recognized by the Church as the Bishop of Rome. But, in times past, the process of naming the Bishop of Rome was not as clearly defined as it is today.
The biggest crisis in Papal history arose during the Western Schism, which spanned a 40 year period (1378 to 1418). It started shortly after the Avignon Exile, when the Cardinals elected Urban-6 as Pope (he happens to be the last guy elected Pope who was not first a Cardinal). This proved to be an unpopular choice, so just five months later, the same guys that elected Urban-6 elected Clement-7 as “pope.” Forty years of anti-Popes ensued. The Catholic Church has never defined who was the “real” Pope during this period (or if anybody was), so every “pope” during this period is really an anti-Pope. The schism was ended (forty years later) by the Ecumenical Council of Constance, which deposed (not two, but three) papal claimants, and elected Martin-5. But nobody is sure of HIS validity, because we don’t know if any of the three deposed “popes” was really Pope.
So, for forty+ years, the Catholic Church has ABSOLUTELY NO IDEA who was Pope (or if anybody was Pope). If the Church “knows,” She has never made this known to us.
Fortunately for the Church, this does not matter. There is no such thing as Papal succession. A Pope does not inherit his authority from his predecessor (just as a US President does not inherit authority from his predecessor). The authority is attached to the Office, not to the previous guy.
We have had anti-Popes before, and we could have them again. But it is not really a crisis for the survival of the Church. It is an unfortunate situation, but the Church has dealt with MANY unfortunate situations. The Church that Our Lord established remains, and will remain.