The concept of hyperspace ( multi dimensions ) can be used to travel a long distances in the universe by curving the 4 dimensional space-time. The space-time separating the two points in universe is curved in a higher dimension so that the 2 points come close to one another. Thus making the travel in our universe less time consuming
This concept can be better understood by considering a flatlander ( 2 dimensional being ) living on a rectangular paper. This flatlander can move only along the 2 dimensional paper ( front, back, left, right ) and cannot visualize the 3rd dimension ( up, down ). He has to travel from one corner of the paper to another. He has to travel along the diagonal for this. But if he can find some technology to curve the paper ( in 3rd dimension- upwards ) and bring the 2 corners close to one another, then he can walk off from one corner to another directly and avoid traveling along the diagonal. Thus his journey becomes shorter.
This concept when extended to our 4 dimensional universe requires the space-time to be bent in a higher dimension. The energy required to do this is enormous. We have not yet developed the technology required. This curving of space-time is similar to the opening of worm holes and like teleporting seen in the movies. But in reality we are far away from achieving this.
