In a perfect square wave the amplitude would rise from zero to maximum in zero time. However we live in the real world - to do this in reality would require a perfect system with infinite energy! So in real systems we can never create a perfect square wave and it takes a certain finite time for the amplitude to move from zero to maximum. This time is called the rise time. This is a simplified definition because engineers use a more rigorous mathematical description which is not quite the same thing, but you can consider it in the way described to get an idea of what engineers are talking about in general. The faster the rise time, the closer you are to a perfect square. The reverse of the rise time (the time taken to fall from maximum to zero amplitude) is called the fall time.

Engineers working with modern Rife type machines tend to aim for the fastest rise and fall times possible in practice because this gives a greater content of very high frequency harmonics which may be beneficial to the biological effect.