The simple answer is that all the current (and thus all the power) is drawn at the peaks of the sin wave. This means for most of the sin wave no current is being drawn. This is a problem because now the average power rating that a power plant can produce -- where the power is produced for all parts of the wave in roughly equal amounts -- is no longer enough, they have to be able to generate much more power just for the peak of cycle.
The term "load inbalance" is most commonly used in three phase systems where ideally the currents on all three phase/outer/hot conductors should add to zero, having no current on the neutral conductor. Having significantly different loading on the three phases will create changes in voltages on the individual conductors and generally not make efficient use of transmission capacity.
Interestingly, having a lot of switching power supplies with poor power factor correction on a three phase network (e.g. in an office building) will also create currents on the neutral, but with three times the network frequency (and harmonics), as during one cycle, the current for the peaks caused by...
This load imbalance is a large problem.