In your brain, your neurons have axon terminals that wave to and fro like seaweed occasionally making contact with other neurons. (Memory is the connection between two or more neurons.) When contact is made and an action potential is generated from one neuron, the receiving neuron may also be activated and create its own action potential. Thus, you have activation of that memory.
Now, how quickly synapses and how many synapses are formed depends on many factors. One factor is the intensity of the neural signal - the number of action potentials...
Background info:
An action potential is all-or-nothing; an electro-chemical signal is either sent from a neuron or it isn't. Like a light switch, it's either on or off. A single AP is very weak and may not be enough to trigger an AP in the receiving neuron(s). However, its frequency determines how intense the signal. The more frequent the AP, the stronger the signal, and the more likely the receiving neuron(s) will also be activated and send its own AP.
What happens to the axon terminals under increased intensity (more AP) is that they become more excited and wave to and fro faster, potentially making more contacts with neighboring neurons. However, once contact is made (a synapse is formed), it can just as easily lose it... unless, (and I'm speculating here on a not fully understood process) unless that synapse triggers an AP in the receiving neuron. At this point, something happens chemically which makes that synapse stable (thought not necessarily permanent) and allows for the continued communication between the two neurons.
So why speed? Speed requires increased number of AP just as loud and firm do. (I'm not necessarily referring to the activation of fast-twitch muscle fibers responsible for fast movements, just in the rate of neural signals in the brain.) The more AP, the more synapses can potentially form. This essentially strengthens the memory. We are only concerned with memorizing the piece, not the technique of playing.