Peter approached Jesus and asked him, “Lord, if my brother sins against me, how often must I forgive? As many as seven times?” Jesus answered, “I say to you, not seven times but seventy-seven times.”
While Peter was already being fairly generous in offering to forgive his brother seven times, our Savior insists that forgiveness must be unconditional – and this was the meaning of his words: And if he sin against thee seven times in a day, and seven times in a day be converted unto thee, saying, I repent; forgive him. (Luke 17:4)
In response to Peter’s question, the good Jesus uses the number “seven” to convey the totality of forgiveness. While Peter considered “seven” solely as according to the letter, the Savior raises our hearts and minds to the recognition of the true spirit of his words. Many translations render our Lord’s words not as seventy-seven times, but as seventy times seven times (i.e. four hundred ninety times).
There is a great mystery hidden in these numbers.
Seven times, meaning totality
St. Peter had understood our Lord’s words narrowly, as though “seven times” were the limit of forgiveness. However, the Savior makes it clear that “seven” signifies not so much the literal number, but rather the figure of totality.
Just as there are seven days in the week, so too all of time is included in the number seven. And in the recurrence of the seven day week, so too is included also all the sins that could fill those seven days. Hence, when our Lord had said, If he sin against thee seven times (Luke 17:4), he meant, “Whatsoever your brother may do against thee and howsoever he may sin against thee.”
Fr. Cornelius a’ Lapide offers this comment: “But Peter did not clearly understand whether seven times were to be taken definitely for the precise number seven, or whether it were to be taken indefinitely for as often as might be needed. He asks therefore Christ to explain His meaning, and to tell him exactly how often he was to forgive his brother his trespasses. Peter’s breast was narrow as yet carnal, and bounded by the flesh. He could not understand the infinite abyss of mercy which there was in the Divine nature of Christ.”
...Seventy times seven times, the prophecy of Daniel
If our Savior said, seventy times seven times (i.e. four hundred ninety times), this signifies “times without number” – for not only must we forgive every type of sin, but we must forgive every sin any number of times.
St. Hilary sees an allusion to Lamech (whose sins were great so as to incure the divine wrath), Sevenfold vengeance shall be taken for Cain: but for Lamech seventy times sevenfold. (Genesis 4:24) Thus, though the sins of men have mounted on and on without number, the Lord continues to forgive all those who are contrite and beg his mercy.
There is another mystery hidden in the number “seventy times seven”.
 As I was yet speaking in prayer, behold the man Gabriel, whom I had seen in the vision at the beginning, flying swiftly touched me at the time of the evening sacrifice.  And he instructed me, and spoke to me, and said: O Daniel, I am now come forth to teach thee, and that thou mightest understand.  From the beginning of thy prayers the word came forth: and I am come to shew it to thee, because thou art a man of desires: therefore do thou mark the word, and understand the vision.  Seventy weeks are shortened upon thy people, and upon thy holy city, that transgression may be finished, and sin may have an end, and iniquity may be abolished; and everlasting justice may be brought; and vision and prophecy may be fulfilled; and the saint of saints may be anointed.  Know thou therefore, and take notice: that from the going forth of the word, to build up Jerusalem again, unto Christ the prince, there shall beseven weeks, and sixty-two weeks: and the street shall be built again, and the walls in straitness of times. (Daniel 9:21-25)
From the Douay-Rheims commentary:
 "The man Gabriel"... The angel Gabriel in the shape of a man.
 "Man of desires"... that is, ardently praying for the Jews then in captivity.
 "Seventy weeks"... Viz., of years, (or seventy times seven, that is, 490 years,) are shortened; that is, fixed and determined, so that the time shall be no longer.
 "From the going forth of the word"... That is, from the twentieth year of king Artaxerxes, when by his commandment Nehemias rebuilt the walls of Jerusalem, 2 Esd. 2. From which time, according to the best chronology, there were just sixty-nine weeks of years, that is, 483 years to the baptism of Christ, when he first began to preach and execute the office of Messias.-- Ibid.
 "In straitness of times"... angustia temporum: which may allude both to the difficulties and opposition they met with in building: and to the shortness of the time in which they finished the wall, viz., fifty-two days.
 And after sixty-two weeks Christ shall be slain: and the people that shall deny him shall not be his. And a people with their leader that shall come, shall destroy the city and the sanctuary: and the end thereof shall be waste, and after the end of the war the appointed desolation.  And he shall confirm the covenant with many, in one week: and in the half of the week the victim and the sacrifice shall fall: and there shall be in the temple the abomination of desolation: and the desolation shall continue even to the consummation, and to the end. (Daniel 9:26-27)
Again, from the Douay-Rheims Bible Commentary:
 "A people with their leader"... The Romans under Titus.
 "In the half of the week"... or, in the middle of the week, etc. Because Christ preached three years and a half: and then by his sacrifice upon the cross abolished all the sacrifices of the law.-- Ibid.
 "The abomination of desolation"... Some understand this of the profanation of the temple by the crimes of the Jews, and by the bloody faction of the zealots. Others of the bringing in thither the ensigns and standard of the pagan Romans. Others, in fine, distinguish three different times of desolation: viz., that under Antiochus; that when the temple was destroyed by the Romans; and the last near the end of the world under Antichrist. To all which, as they suppose, this prophecy may have a relation.