What does orthogonality mean in the context of adjacent channels in a filter bank?
The mathematical definition of orthogonality between two vectors is that their dot product is zero.  It just means that there is no correlation between the two- at least at that "phase".  It is often the case that if you shifted one of the vectors you would get strong correlation.

Infinite vectors of different frequencies are always orthogonal, so in an ideal world the output of adjacent channels in a filter band would always be orthogonal.  There are two ways, though, that the real world is not ideal.

First, time limitations can introduce non-orthogonality.  The non-orthogonality is usually trivial if both of the vectors have "many" sinusoidal cycles, but can be substantial if the length is less than a cycle.

Second, non-ideal filters means that attenuated stop-band frequencies get into the filter output, which means that the adjacent channels do have frequencies in common, just at different amplitudes.