Jesus performed miracles that never can be duplicated. They demonstrated his deity. They were miracles like raising Lazarus from the dead, walking on water, feeding of the 5,000, the miraculous catch of fish, etc.
The Apostles were able to heal the sick, give sight to the blind, cast out demons, and occasionally raise the dead. They also had the power to do miracles. These miracles were signs given to them to verify that they were indeed true Apostles of Christ, and that their message was the true message of Christ. Here is what the Bible says:
2 Corinthians 12:12 Truly the signs of an apostle were wrought among you in all patience, in signs, and wonders, and mighty deeds.
Hebrews 2:3-4 How shall we escape, if we neglect so great salvation; which at the first began to be spoken by the Lord, and was confirmed unto us by them that heard him;
4 God also bearing them witness, both with signs and wonders, and with divers miracles, and gifts of the Holy Ghost, according to his own will?
"By them that heard him" is a direct reference to the Apostles. Signs and wonders, miracles and the gifts of the Holy Spirit were given specifically to the Apostles as a sign that they were the true Apostles and that their message was the true message from God.
Primarily it was to convince the Jews. Especially the gift of tongues:
1 Corinthians 14:21-22 In the law it is written, With men of other tongues and other lips will I speak unto this people; and yet for all that will they not hear me, saith the Lord.
22 Wherefore tongues are for a sign, not to them that believe, but to them that believe not: but prophesying serveth not for them that believe not, but for them which believe.
I will speak unto "this people" which is Israel. He quotes out the law, specifically Isaiah 28. The "wherefore" of verse 22 connects the two versese together. Tongues are a sign to unbelieving Jews. That is the context. It is a sign to the unbelieving Jews of the first century by the Apostles to whom they were given.
In the three instances of speaking of tongues given in the book of Acts--chapters 2, 10, and 19, all three of these events had these conditions present.
History tells us that by the end of the first century tongues had ceased. They had served its purpose. The Jews had rejected the signs and miracles, and tongues in particular, and judgment came upon them in the form of Titus destroying Jerusalem and in particular their Temple. And Israel was thus scattered. The prophecy in Isaiah 28 had been fulfilled.
1Cor. 13:8 tells us that tongues, prophecy, and (revelatory) knowledge would cease, and they did.
Now:
Hebrews 1:1-2 God, who at sundry times and in divers manners spake in time past unto the fathers by the prophets,
2 Hath in these last days spoken unto us by his Son, whom he hath appointed heir of all things, by whom also he made the worlds;
God spoke in different ways in OT times to His people--visions, audibly, dreams, theophanies, etc.
Now, in these last days God speaks to His people through His Son. Who is that? He speaks to us through His Word which reveals to us His Son. Everything that we need to know about Jesus Christ is contained in the NT, which was written down by eyewitnesses of the Lord.
The Apostles are dead; but the Word of God lives on forever, especially the words of our Lord, and his apostles.
