Treading water or water treading is what a swimmer can do while in a vertical position to keep their head above the surface of the water, while not providing sufficient directional thrust to overcome inertia and propel the swimmer in any specific direction.
As such, the phrase "treading water" has become a euphemism for an effort expected to create motion, but which actually results in merely staying in one, possibly barely sustainable, place.
Any sort of movement that allows the swimmer to do this can be classified as treading water, but it is more efficient to move the arms and legs in a specific fashion.
Drowning non-swimmers often splash and kick in an effort to stay above the surface but their lack of technique along with shortness of breath and the panic factor make this a very ineffective method of treading water. They will usually tire quickly and not be able to stay above the surface very long.
More experienced swimmers often find their own method of staying above the surface. These techniques often involve sculling, flutter kick, and other unofficial techniques of staying above the surface.
The eggbeater kick is a highly refined and efficient method of treading water. It involves the swimmer in a "sitting position" in the water. The swimmer's back must be straight, knees bent so that the thighs are parallel to the surface of the water, and lower legs perpendicular to the surface.
The left foot makes a clockwise motion while the right leg makes a counterclockwise motion towards the axis of the body. The legs should never meet because when one foot is on the inside of the motion, the other should be on the outside. The arms are not involved directly in this kick.
The most critical aspect to having an effective egg beater kick is flexibility. You need very good range of motion of the hips to have a good egg beater kick.
Eggbeater kick can be used to move through the water if the body is angled. Because of the opposite motion of the legs, eggbeater is a very smooth and steady way of treading water. It also leaves the hands free to do work if necessary.
This method of treading of water is the preferred method used by lifeguards and other aquatic rescue professionals because of its efficiency and simplicity. The fact that it does not occupy the hands is a major factor in this preference as these professionals often have to perform first aid as they are swimming to safety.