How does a current mirror produce an amplified current? What is the physical process behind it?
You can just think of a larger MOSFET as multiple MOSFETs in parallel. The following current mirror circuit will sink 10mA per output MOSFET for a total of 20mA, doubling the input current.







simulate this circuit &ndash; Schematic created using CircuitLab

A MOSFET with a channel width of \$n × W\$ will behave the same as \$n\$ MOSFETs with channel width \$W\$ in parallel.