There is no doubt that a cantilevered staircase is one way of making a major visual impact.
To the casual observer a cantilevered staircase appears to be floating because it overhangs without any external bracings or supports. What holds it up is a counterweight hidden in the wall, out of sight.
Available in straight, quarter turn, half turn, helical and curved formats, it is usually the state of the walls and the position of the staircase that will dictate the type of underlying or hidden supporting structure used. A cantilevered helical stair can support the treads from a central column.