What are the use of these diodes?
These diodes are for temperature compensation.

As there is a diode connection between the Base and Emitter terminals on the transistors, to compensate for any characteristic changes with changes in temperature the diodes are put in place to match these characteristic changes.  

For example: Say that the voltage drop over the diodes increase due to a change in temperature. Without the second matching diode, the voltage over the emitter resistor would change and thus cause a change in the current being drawn, not too helpful when you are using a constant current source. But say that the second matching diode is in place, then any changes to the transistor diode, will be matched by this extra one. So the voltage drop over this diode will increase, thus causing the voltage at the anode of the diode to be greater and furthermore the voltage at the base of the transistor to increase, thus matching the change that occurs to the B-E diode and keeping the voltage over \$R_{E}\$ constant which keeps the current constant.