I'll expand a little but I think much of it is on the forum already;
The six harmonies are split into the internal 3 and the external 3. They are things which much be in harmony for your Kung fu to be effective whatever its goal.
The 3 external harmonies are that the hand and foot move in co-ordination, as do the elbow and knee, as do the shoulder and hip. You will notice in shaolin form rarely do we stand in one stance and do a lot of hand moves. This is because every movement of the upperbody is co-ordinated with the lower. This means Shaolin has a very active footwork.
The 3 internal harmonies are far more interesting and vary according to the specific sect of Shaolin. I will not reveal the various different versions however I will state the standard version (not strictly from Shaolin but common accross china):
Qi Yu Li He ---- Breath/sensation and physical power in harmony
Yi Yu Qi Ye ---- 'Conscious Intent' and breath/sensation in harmony
Xin Yu Yi He ----- 'unconscious instinctual mind' and 'conscious intent' in harmony
Xin Yu Yi He is the ultimate goal of training Kung Fu. These profound harmonies are not just in Martial technique but in life in general.
The 6 harmonies are part of shaolin theory:
1 truth, 2 extremes, 3 sections, 4 sensations, 5 elements, 6 harmonies, 7 stars, 8 words etc.