What in neurons and their connections changes during the process of learning?
What changes in the process of learning:


The connections (the way one neuron is connected to another). New synapses can form or dissolve in the process of learning. The glial cells such as astrocytes and microglia can facilitate this process.
Strength of connections: Existing connections can be made weaker or stronger in the process of triggering the same circuit. This happens by up/down regulation of the ion channels at the synaptic junctions.


This process is not fully understood and is an active area of research. You can find some mathematical models too for learning processes such as Long Term Potentiation etc.