During the Buddha's time, he had also performed "miraculous feats" like emitting fire on one side of his body and water on the other side. He had what we called supernatural powers. In our daily lives we have either witnessed or experienced unusual events. In fact most of these unusual events in the end could be explained rationally. That leaves only a very few unexplainable events. Buddhists are aware of the existence of beings in other planes of existence. Some of these beings have special powers over worldly affairs and they may "intervene" in the conduct of our worldly affairs, for some reasons or the other. For lack of a better term, we may say they are like our "guardian angels".
As for miracles performed by Jesus, I think it will be more appropriate if you ask the Christians.