To expand on Tim Prebble's comment, pumping a sine wave through the water causes the hose to move back and forth (well, actually in a kind of circular pattern, but that's not really important). Since the end of the hose is oscillating back and forth, the water makes a zig-zag pattern, similar to what happens if you wave a hose back and forth by hand.
The hose is oscillating at a rate of 24 times per second, since 24 Hz is the frequency of the sine wave being played. If you film it with a camera that films a number of frames per second equal to the frequency of the sine wave, it will always capture the image at exactly the same point on the sine wave, resulting in the illusion of the water always being in the same zig-zag-y shape, instead of continually falling away from the hose nozzle.
The 23 Hz and 25 Hz variants just put the sine wave slightly out of sync with the camera, so that a slightly earlier or later part of the oscillation is captured each frame. The actual motion of the water is unchanged.
You can sometimes see a similar effect when watching film footage of a car accelerating - If the wheels seem to stop spinning or move in reverse, it's because the number of revolutions per second have exceeded the frames per second of the camera.