Conversion

Literally a "turning towards", used of a turning towards God or the Church of God - either, in the case of Catholics, from sin or life of sin, or, for others, from previous heresy or unbelief. The latter indicates a turning to the Church from without and an acceptance of Her doctrine and discipline. (Definition from A Catholic Dictionary, 1951)

Some Clergy and laity today will attempt to say conversion of non-Catholics is no longer essential. See references in Scripture and past Church teaching below to see that this is far from being the case!
 

References in Scripture:

• "Go ye into the whole world, and preach the gospel to every creature. He that believeth and is baptized, shall be saved: but he that believeth not shall be condemned." Matthew 16:15
• "But Peter said to them: Do penance, and be baptized every one of you in the name of Jesus Christ, for the remission of your sins: and you shall receive the gift of the Holy Ghost....They therefore that received his word, were baptized; and there were added in that day about three thousand souls" Acts 2:38,41
   

Church Teaching on Conversion:

• "During the barbarian invasions of the Middle Ages, we see men and women of royal rank and even workmen and valiant Christian women of the common people using every endeavor to convert their fellow citizens to the religion of Jesus Christ and to fashion their morals according to its pattern, so as to safeguard both religion and the state from approaching danger" Encyclical on Promotion of Catholic Missions, 1951
• "We reflect upon those immense regions of the Indies where for many centuries men of the Gospel have expended their labor. Our thoughts turn first of all to the blessed Apostle Thomas who is rightly called the founder of preaching the Gospel to the Hindus. Then, there is Francis Xavier, who long afterwards dedicated himself zealously to the same praiseworthy calling. Through his extraordinary perseverance, he converted hundreds of thousands of Hindus from the myths and vile superstitions of the Brahmans to the true religion. In the footsteps of this holy man followed numerous priests, secular and religious, who with the authority and permission of the Holy See strove untiringly to preserve and promote the Christian mysteries and institutions introduced by Thomas and renewed by Xavier. To this day, they are continuing these noble efforts; nevertheless, in the vast reaches of the earth, many are still deprived of the truth, miserably imprisoned in the darkness of superstition! How very great a field, especially in the north, lies yet uncultivated to receive the seed of the Gospel!
  Pondering these needs, We place our trust in Our Savior who alone knows the exact circumstance and time to bestow his light; he is wont to direct the mind and hearts of men by divine inspiration. But, assuredly, We ought to exert every possible effort to convert such a great part of the world." Encyclical On Seminaries for Native Clergy by Pope Leo XIII, 1893
• "On the other hand, such a pious practice leads to the hope that these children, who have been trained to pray for the conversion of the heathen from the first moment when the flower of charity begins to bud in their young and tender hearts, may, with the help of God, themselves receive a vocation for the apostolate, a vocation which if it is nurtured with care may perhaps in time supply capable workers for the mission field" Encyclical on Catholic Missions by Pope Pius XI, 1926
• "St. Francis, "a man who was truly Catholic and apostolic," in the same admirable fashion that he had attended to the reformation of the faithful, so likewise set about personally and commanded his disciples to occupy themselves before everything else with the conversion of the heathen to the Faith and Law of Christ. Nor need We dwell at length on a subject so well known to all" Encyclical On St. Francis of Assisi by Pope Pius XI, 1926
• "Both history and experience teach that when once the rulers of a people have been converted to Christianity, the common people follow closely in the footsteps of their leaders." Encyclical On Catholic Missions by Pope Pius XI, 1926
• "Finally, gravely advise those who have converted from Mohammedanism or the children of such converts, if they lack confidence in their constancy in the Faith, fearing punishment by their rulers if they abandon their Turkish names, to emigrate secretly from those territories and come for refuge to Christian lands" Encyclical On Christians Using Mohammedan Names by Pope Benedict XIV, 1754
• "By virtue of Our apostolic authority We define and declare by these present letters, or by any translation thereof signed by any notary public and sealed with the seal of any ecclesiastical dignitary, which shall thus command the same obedience as the originals, that the said Indians and other peoples should be converted to the faith of Jesus Christ by preaching the word of God and by the example of good and holy living." Pope Paul III (Topic: the enslavement and evangelization of Indians 1537)
• "By these salutary instructions it desires to provide measures whereby Jews and other infidels may be converted to the orthodox faith and converts may remain steadfastly in it" Council of Basil 1431-1435
• "Thus, then, as the heavenly spirits with perfect unanimity exalt and glorify God, so do we pray that the same be done over all the earth; that all nations may come to know, worship, and reverence God; that all without a single exception may embrace the Christian religion, may devote themselves wholly to the service of God, and may be convinced that in Him is the source of all sanctity and that there is nothing pure, nothing holy, that does not proceed from the sanctity of His divine name. According to the testimony of the Apostle, The church is cleansed by the laver of water in the word of life. and the word of life signifies the name of the Father and of the Son and of the Holy Ghost in which we are baptised and sanctified.
  And since there is no expiation, no purity, no integrity, in him over whom the divine name has not been invoked, we desire and pray that all mankind may abandon the darkness of their impious infidelity, and, enlightened by the rays of divine light, may come to recognise the power of this name and look to it alone for true sanctity, and that thus receiving the Sacrament of Baptism in the name of the holy and undivided Trinity, they may receive the plenitude of sanctity from the right hand of God Himself." Catechism of Council of Trent, The First Petition of the Lord's Prayer: Hallowed be Thy Name, That Unbelievers May Be Converted
• "Infidels, on the contrary, are not members of the ecclesiastical society, according to the words of St. Paul: Quid mihi de his qui fortis sunt, judicare? (I Cor., v, 12); they are entirely exempt from the canon law; they need to be enlightened and converted, not punished" Catholic Encyclopedia 1917, Infidels
• "The Church, mindful of the order of the Saviour: Go, teach all nations (Matt., xxviii, 12), has always considered the preaching of the Gospel among the infidels and their conversion by her apostolic missionaries to be one of her principal duties" Catholic Encyclopedia 1917, Infidels
• "Doubtless, we still are far from having but one fold and one shepherd ; nevertheless, there is not to-day a province or race of men so remote, but has not heard the name of Him by whom all men must be saved and has given children to the Church. The work of the missions is placed, as is well known, under the care and direction of the congregation of cardinals that bears the admirable name Da Propaganda Fide (for the propagation of the Faith), instituted by Gregory XV in 1622. Ever encouraged and developed by the popes, it is the directing body on whom the evangelical labourers in infidel lands depend. It sends them forth and grants them their powers, it established the prefectures Apostolic and the vicariates, and it is the tribunal to whose decision the missionaries submit their controversies, difficulties, and doubts." Catholic Encyclopedia 1917, Infidels
• "To draw the infidels to the Faith, the missionaries ought, like St. Paul, to make themselves all things to all men, adopt the customs of the country, acquire the native language, establish schools and charitable institutions, preach especially by their example, and show in their lives how the religion they have come to teach is to be practiced (cf. Instr. of the Prop. to the Vicars Apostolic of China, in the Collectanea S. C. de Prop. Fide , n. 328)." Catholic Encyclopedia 1917, Infidels
   

Summary

It is well known that the entire history of the Catholic Church consists of missionaries and martyrs dedicating their lives to converting others to the true faith, undergoing the most cruel and unspeakable tortures and death as a result. Yet some Catholics today will actually say conversion is no longer important, which is an insult to Our Lord's passion and death, to the lives of the Apostles, and to the 20 centuries of missionaries and martyrs of the Church whose sole goal was to convert others to Catholicism!

Scripture and past Church teaching speak for themselves - let no Catholic ever say conversion is unimportant, for those outside of the true Church of Christ cannot be saved.