This is an excellent question and one that reveals something about God to us. Jesus performed a number of different types of miracles including healings, exorcisms, raising the dead, miraculous provision of food and control over nature. And when Jesus performed these miracles people wondered who this Jesus was. In other words rather than ask how he could do miracles, they wanted to know who he was that he was able to do miracles (See Mark 4:35-4:41 for an example).
The general understanding of Jesus’ contemporaries was that he must have been sent by God or else he would have been unable to perform miracles (John 3:1-2). Jesus’ greatest enemies were more perceptive however. They recognised that Jesus’ miracles and his claims could only be true of God himself (Luke 5:17-21, John 5:16-18). Despite this recognition they considered Jesus to be blasphemous for claiming to be God when he was obviously human. Yet ultimately the Christian witness is that Jesus came to earth as God in the flesh (Philippians 2:5-11) in order to reconcile humanity to himself (Colossians 1:15-20).
Hence the reason that Jesus is able to perform miracles is that he is God. Only the God who created the world is able to perform miracles within the world. As to miracles performed by followers of Jesus, these are works of God in the lives of believers (Acts 9:34 is a clear example).
The reason why Jesus performed these miracles is given to us in John 20:30-31
“Jesus did many other miraculous signs in the presence of his disciples, which are not recorded in this book. But these are written that you may believe that Jesus is the Christ, the Son of God, and that by believing you may have life in his name.”
Jesus performed these miracles because he is God and wanted to demonstrate that his death and resurrection is the means by which he reconciles a rebellious humanity to himself. I hope this helps you to be reconciled to him also.