Well, with a 3-axis CNC machine, the spindle moves up and down, side to side, back and forth. 5-axis machines, in addition to this 3-axis movement, have two further axes in play: either the table rocks side to side on two different axes or the spindle itself swivels on two axes.
Either of these methods (more on their differences later) allow the cutting tool to approach the workpiece from an infinitely greater number of angles, and this makes it possible to create highly complex shapes.
It also reduces the number of setups needed: machinists don’t have to manually turn the workpiece over, because the cutting tool can simply reach more places. And this makes the entire machining process much, much faster.