Muscle memory is a term that is thrown around with reckless abandon lately.
Russyruss gave you the true definition, that of neural recruitment/programming, starting in the motor cortex of the brain, and travelling down the spinal cord and to the effector muscles. Beyond the motor programming that occurs in the CNS, adaptations also occur in the periphery. With strength training the motor nuerons can carry impusles of geater intensity, the neuromusclar junction increases in size and efficiency, and that these adaptations appear to be fairly permanant (see citations at bottom).
When it comes to hypertrophy, another explanation that has been suggested (I believe by doggcrap) to explain the quick return in gains following detraining is due to the previous stretch in myofascia. Again, this is just a theory, and would be quite hard to prove or disprove via scientific study.
Russy, with regards to the biochemical adaptation that accomany resistance traning, the intensity, length of sets, and work:rest ratios of the training has to be taken into consideration. Training purely for strength is going to tax the CP system, and the majority of biochemical adaptations that occur will be increasing intracellular levels of creatine phosphate (fuel) and the enzymes creatine kinase, ATPase, and perhaps myokinase.
When sets last longer than 30 seconds, however, and especially when rest periods are short, then there is likely to be a greater adaptation in the anaerobic glycolytic system. As such, you would expect to see increases in glycogen storage, glycogen synthase, and glycolytic enzymes, as well as perhaps an increase in intramuscular H+ buffering.
Br