Perhaps the following quotes from a couple of commentaries will help answer your question.
First from The Bible Knowledge Commentary:
13:9-10. As Paul explained it, the gift of knowledge (v. 8), essential as it was, was not exhaustive. The ability to prophesy, however crucial for the church’s life, was of limited scope. The gifts were temporary blessings in an imperfect age. One day they would give way to perfection, toward which all the gifts pointed. What Paul meant when he referred to the coming of perfection is the subject of considerable debate. One suggestion is that perfection described the completion of the New Testament. But verse 12 makes that interpretation unlikely. A few have suggested that this state of perfection will not be reached until the new heavens and new earth are established. Another point of view understands perfection to describe the state of the church when God’s program for it is consummated at the coming of Christ. There is much to commend this view, including the natural accord it enjoys with the illustration of growth and maturity which Paul used in the following verses.
13:11. Paul elsewhere described the purpose of gifts by an illustration employing the imagery of growth and maturity. According to Ephesians 4:11-16, the gifts were to be used to bring the church from a state of infancy to adult hood. The word translated “mature” in that passage (Eph. 4:13) is the word translated “perfection” (teleion) in 1 Corinthians 13:10. In the Ephesians passage, maturity is defined as “attaining to the whole measure of the fullness of Christ.” Such a state will obviously not exist until Christ’s second coming. It would appear that the same perspective was developed in this passage to the Corinthians. Paul applied the illustration to himself (cf. vv. 1-3). The threefold talking, thinking, and reasoning were probably meant to balance the thrice-mentioned gifts (v. 8). With the coming of adulthood, such gifts become passe . Paul’s use of the word became (gegona, a perf. tense verb, probably proleptic; cf. Rom. 13:8; 1 Cor. 14:23) was of course to be understood in the context of the illustration. It does not indicate that he personally or the church collectively had yet arrived at that point (cf. Phil. 3:12). It would not, on the other hand, necessarily rule out a gradual obsolescence of certain gifts as the church progressed toward maturity.
13:12. A city like Corinth, famous for its bronze mirrors, would have particularly appreciated Paul’s final illustration. The perfection and imperfection mentioned in verse 10 were deftly likened to the contrasting images obtained by the indirect reflection of one’s face viewed in a bronze mirror and the same face when viewed directly. Such, Paul said, was the contrast between the imperfect time in which he then wrote and the perfect time which awaited him and the church when the partial reflection of the present would give way to the splendor of perfect vision. Then Paul would see God (cf. 15:28; 1 John 3:2) as God now saw Paul. Then partial knowledge (cf. 1 Cor. 8:1-3) would be displaced by the perfect knowledge of God.
13:13. Paul completed his three-paneled portrait of love (vv. 1-3, 4-7, 8-13) with a final triad: faith, hope, and love. Much discussion has focused on whether faith and hope were portrayed by Paul as being (with love) eternal. The solution is probably found in verse 7. Faith is an expression of love (the word “trusts,” pisteuei, v. 7, is the verb form of the noun “faith,” pistis), as is hope (cf. Gal. 5:5-6). Faith and hope, as manifestations of love, will endure eternally. So too everyone who follows the way of love (1 Cor. 14:1) finds “the most excellent way” (12:31b), because every individual characterized by love carries that mark eternally. The spiritual gifts will one day cease to exist, but love will endure forever.
(3) Priority of prophecy to tongues (14:1-25). Chapter 13 is one of the most sublime digressions in any letter in any language. But it was nonetheless a deviation from the central theme of gifts and their use by the church which Paul began in chapter 12 and then concluded in chapter 14. Paul had intimated in chapter 12 that the Corinthians were perverting the purpose of gifts from a unifying influence on the church to one fostering fragmentation and discord (esp. 12:21-25). A contributing factor to their factious spirit was the Corinthian pursuit of individual freedom and personal enhancement at the expense of other members of the body whose needs may have been trampled or ignored along the way. Manifestations of this self-centeredness affected each of the problem issues taken up since chapter 8.
The focal problem in the matter of the use and abuse of gifts seemed to be the Corinthian fascination with tongues, a gift which apparently lent itself most readily to perversion from something intended “for the common good” (12:7) to something employed for personal enhancement (14:4). Paul’s corrective was not to stifle the use of gifts (14:39; cf. 1 Thes. 5:19-20) but to urge that their use be regulated by love. The gifts of the Spirit should be controlled by the fruit of the Spirit, chief among which was love (Gal. 5:22). This would lead to exercising the gifts so they would benefit the church body as a whole (14:5) and also honor God (14:25, 33, 40). By way of illustration and correction, Paul compared and contrasted the Corinthians’ preoccupation with tongues with their apparent disinterest in prophecy.
In his study Bible, Charles Ryrie has the following to say about verse 11:
There are stages of growth within the present imperfect time before Christ’s return. After the church began, there was a period of immaturity, during which spectacular gifts were needed for growth and authentication (Heb. 2:3-4). With the completion of the NT and the growing maturity of the church, the need for such gifts disappeared.
We should note that Paul makes a distinction between the disappearance of the gifts of prophecy and knowledge and that of tongues. This is done using different Greek words and voices. With prophecy and knowledge, he used a word in the passive voice which meant “to be rendered inoperative.” Note also verse 9. But with tongues he used the middle voice and a word that meant “to cease.” The middle voice suggest that this gift would gradually die and disappear on its own. Probably because its primary purpose as a sign to the Jews (see chapter 14:20f) would cease after the fall of Jerusalem. This of course is debated.