Measures of central tendency determine a value that is most likely to occur. Now this can be described by three different values. The arithmetic mean present you with an approximate answer that is close to the central value and hence is a good indicator of the central tendency. The mode is the most commonly occurring value and is again an indicator of central tendency.
The median is the middle value of the group and often it lies around the central value. This gives it a good value as an indicator of central tendency. However, the geometric mean wanders off from the central tendency and is not a good measure of the central tendency.