Once you turn on node editing, you can manipulate the various nodes and curve handles. A selected a node can be dragged and dropped anywhere on the canvas and, in fact, outside the canvas. Multiple nodes can be selected to be dragged in unison by either drag-selecting or selecting individual nodes while holding down the Shift key. Note that curve handles can't be addressed in multiple node selections.
You can adjust the curve handles in a similar fashion by dragging them in or out to shorten or lengthen them, or in a new direction to change the angle of the curve, or both. One end of the curve handle on a given node controls the portion of the segment on that side of the node, the other side of the segment is controlled by the end on the other side of the node.