"A goalkeeper is considered to be in control of the ball when:
• the ball is between the hands or between the hand and any surface
(e.g. ground, own body)"
So a hand touching the ball AGAINST the ground, goalpost, own body is control. A hand tounching the side of the ball on the ground is not (balls needs to be BETWEEN hand and surface.
"or by touching it with any part of the hands or arms"
i.e. any part of BOTH hands or arms (thanks GraemeS)
"except if the ball rebounds accidentally from the goalkeeper or the
goalkeeper has made a save"
So any two handed punches or double handed saves are not counted as control.
So this part of the Law has defined what is control when TWO surfaces (hand, arms, ground etc) are involved. It then goes on to make it clear what constitutes control with less than two: control is still established when:
"• holding the ball in the outstretched open hand" i.e. Just one surface.
"• bouncing it on the ground or throwing it in the air" No surfaces at all
A goalkeeper cannot be challenged by an opponent when in control of
the ball with the hands."
This makes clear consistent sense, and also makes it clear why all the above needed to be included in the Law. So a single hand or finger holding ball to the ground cannot be challenged for. Very sensibly IMO as a goalkeeper down on the ground or lying with one hand on ball is extremely vulnerable to flying boots (which, in the end, is what this Law is trying to protect).
As a former keeper I questioned this law in detail with one of the tutors when I did my course and the above is exactly what he said apart from the "finger on the side of the ball" as his definition was that if any part of the finger was in contact with the upper hemisphere of the ball (including the line) it was deemed to be in control so side would be ok. This is taking the definition to its limit but it was a fun discussion. I don't know the actual law for rugby but I guess it would be a similar definition to downward force when awarding a try.
Obviously in real life there would be no way of knowing for sure if it was that close but it is still one of the laws most players are ignorant of the detail, the general consensus among them and managers is the keeper has to have both hands on it to be in control.