This is one of the most startling promises in the Scriptures. Notice the reason Jesus gives for these greater works. It is because He goes to the Father. And when He goes to the Father, He will send the Spirit. He says later, Unless I go away, the Counselor will not come to you (John I6:7b). He is referring here to the coming of the Spirit. As the Spirit of God comes into human hearts and dwells in them, these things will happen. The Spirit is releasing to us the life of Jesus, so that it is still Jesus who is doing these things.
Some people read this passage and think that we ordinary humans are somehow so capable that we can actually do greater things than the Son of God Himself did when He was here in the flesh. But what He is really saying here is that as the risen Lord, who dwells in us by means of the Spirit, He will do greater things through us than He did when He was here in the days of His flesh.