Neuromuscular Adaptations
When strength training is done correctly, it leads to an increase in mechanical performance (force times velocity). This newly gained "strength" is the result of neuromuscular adaptations. In other words, the body makes neural and/or muscular adaptations. Neural adaptations are movement-specific and can only be transferred between individual exercises to a limited extent. These adaptations take place at the spinal level (in the spinal cord) and at the supraspinal level (in the brain). More strength arises, on the one hand, because the neuromuscular system drives the muscles with more "drive", and on the other hand, through an increase in muscle fibre cross-sectional area.

The increase in strength seen in the first few days can be attributed to the following neural adaptations:
Reduced co-activation of agonists and antagonists (Carolan and Cafarelli 1992)
Increased firing rate of motor units (Duchateau 2006)
Under normal circumstances, recruitment is already maximal during a maximal voluntary contraction. Unlike the increased firing frequency and the reduced co-activation, an increase in recruitment (during maximal contractions) and a synchronisation of the action potentials of the motor neurons involved are not causes of the neurally driven increase in strength. Strength training therefore does not lead to a more synchronised release of action potentials between motor units during muscular contractions. The increase in synchronicity is more likely a consequence of the reduced complexity of the movement (grasping a handle vs. playing the piano).
"Intermuscular coordination", understood as the timed coding of the force (or torque) input of the muscles involved (in terms of timing and force level), is certainly a major factor in determining movement speed. Note that this involves both the activation and the inhibition of muscles.
While it is likely that appropriate training can increase RFD (rate of force development, i.e. the rise in force per unit of time) on a given machine, it remains completely open what physiological significance this has for everyday movements. This has to do with the function-dependent recruitment of motor units.
The next knowledge blog will look at the muscular adaptations of skeletal muscle.
Sources: Carolan B. and Cafarelli E. (1992): Adaptations in coactivation after isometric resistance training. J Appl Physiol 73: 911-917. Duchateau J. (2006): Training adaptations in the behavior of human motor units. J Appl Physiol 101:1766-1775. Strength theory