Why do we use current mirrors?
Current mirrors take a positive current (source) and generate
a negative current (sink).

Current mirrors have low input impedance, so the 'reference' current can be from a poor current source (output impedance 1k ohms) and give rise to a mirrored
current that is a better current source (output impedance 100k ohms).  They isolate the input from variations in the output, so you can wire
together a dozen current mirror outputs to make a summing junction, without
causing any signal flowing back into the input nodes.

The illustrated current mirror makes an excellent pull-down load for
an NPN emitter follower, sinking equal current at a wide range of output
voltages (unlike a resistor pulldown).

The use of two transistors is not required, of course; you could use dozens, and
the single reference input can drive two  parallel output transistors to
make a gain-of-2 mirror, or four to make a gain-of-four mirror (there
are D/A converters built this way).  Integrated circuit operational amplifiers
often use a single current reference and current mirror to generate 
many bias currents.  Matched transistors are very easy to integrate, and
are more accurate than resistors in most IC processes.

Current mirrors with sense-resistor inputs are used as current monitors
high side current sensor as well, with highly attenuated output current.
The low input impedance, like an ammeter, is a major benefit.

Current mirrors have a wide range of uses.