The first gift that Paul mentions here is apostles. He has already referred to them in his letter as part of the foundation of the church (2:20), in the sense that they were directly commissioned by Christ with special authority and who received supernatural revelation from Christ; an example is the apostle John in Revelation 1. That was two of their qualifications; another was that they had to be eyewitnesses of the risen Christ (1 Cor. 9:1). They were also able to perform miracles or what Paul calls ‘the signs of an apostle’ (2 Cor. 12:12). No-one today has all these qualifications.
Then Paul mentions prophets. They too are described as part of the foundation of the church (Eph. 2:20), which means that this type of prophet only existed at the beginning of the church period. From what the New Testament says about them, it seems that they were individuals who were given supernatural revelation and were similar to apostles, except they had not received a direct commission from the risen Christ.
Because they were foundation gifts, there are no apostles and prophets in this sense today, and if anyone comes saying that they are, do not believe them. We have the teaching of the apostles and prophets in the Bible, and we should be very thankful to God for giving it to us. This is not to say that the Lord may not at times reveal secrets to particular individuals, but we are not to call such by terms that the Bible gives to foundation gifts.
Tomorrow we will say something about the next gift Paul mentions, that of evangelists.