Since each subband represents a filtered and subsampled version of the frame component, coefficients within each subband correspond to specific areas of the underlying picture and hence those that relate to the same area can be related. It is most productive to relate coefficients that also have the same orientation (in terms of combination of high- and low-pass filters). The relationship is illustrated below, showing the situation for HL bands i.e. those that have been high-pass filtered horizontally and low-pass filtered vertically.
Figure: Parent-child relationship between subband coefficients
In the diagram it's easy to see that the subsampling structure means that a coefficient (the parent) in the lowest HL band corresponds spatially to a 2x2 block of coefficients (the children) in the next HL band, each coefficient of which itself has a 2x2 block of child coefficients in the next band, and so on. This relationship relates closely to spectral harmonics: when coding image features (edges, especially) significant coefficients are found distributed across subbands, in positions related by the parent-child structure, and corresponding to the original position of the feature. In particular, a coefficient is more likely to be significant if its parent is, and children with zero or small parents or ancestors may have different statistics from children with large parents or ancestors.
These factors suggest that when entropy coding coefficients, it will be helpful to take their parents into account in predicting how likely, say, a zero value is.
By coding from low-frequency subbands to high-frequency ones, and hence by coding parent before child subbands, parent-child dependencies can be exploited in these ways without additional signalling to the decoder.
The wavelet coefficient coding section describes specifically how these relationships are exploited.