Re and the base voltage sets the collector current.
If you keep Vcc at a constant voltage and don’t change the base voltage divider then the emitter voltage stays the same.
If the voltage across the Re stays the same the emitter current stays constant.
If Rc is changed in value, the current through it still stays the same.
Hence, we have a constant current source (within reason).
A better circuit would replace R2 with a zener diode.
If Vcc changes it is less likely to effect the constant current.
If Re was a potentiometer, changing the wiper position would allow you to have an adjustable constant current source.