Hover taxi, air taxi and surface taxi are the three basic ways a helicopter can move around an airport.
The most common of the three is hover taxi. By definition this is operating below 25 feet, however, most hover taxiing is done from the surface to about 10 feet. When deciding on how high to hover taxi there are two main considerations. One is hovering high enough to minimize the danger of catching a skid on a small sign or other low object. Conversely, the other is not hovering too high so that a hovering autorotation can be safely performed in the event of an engine failure. The type of helicopter makes a difference, a high main rotor inertia helicopter like a Bell 206B can safely hover higher than a Robinson R22. Personally, I hover taxi on the higher side because my feeling is that an engine failure is less likely than not seeing an object and catching the skid.
Sometimes you might hear a controller ask a helicopter pilot to air taxi. This is normally done to taxi a longer distance within an airport boundary. The pilot is expected to remain below 100 feet and to avoid overflying equipment and personnel. The pilot should choose an airspeed and altitude combination that is clear of the shaded area of the height-velocity diagram (a chart in the flight manual that depicts airspeed/altitude combinations that supports successful autorotations).
Finally, helicopters with wheels can surface taxi. Since the rotor system only has to produce enough thrust to allow the helicopter to move on wheels (a lot less than hovering) the pilot can taxi closer to objects and buildings without creating a lot of downwash. However, unlike hover and air taxiing, surface taxiing requires a hard surface. Of course, a wheeled helicopter can always hover or air taxi as well.