What is the use of two power supplies in an opamp?
The uA741 does NOT require dual supplies. It requires the ability to bias the operating point of the internal amplifiers between the power supply voltage and the easiest way to achieve that is with a dual supply. Look at the datasheet in section 7.2. Although the supply is shown as VCC+ and VCC- there is no Ground shown. The decision about where the ground point might be is complex and depends on both input bias and output load configuration. For example you could have a load that goes from output to VCC+ which would change the output current characteristics you would expect.  

The biggest problem that new users have is that the 741 is actually a very high voltage op amp, so needs a 10 V (+/-5V) supply to meet the recommended operating conditions.
Notice in section 6.4 that the output swing is guaranteed to be 20 V peak to peak within a 30 V supply (+/-15V). The output amplitude relative to the supply is very restricted, especially as you put a greater load on the output. 

The 741 is used in course material because it is easily analyzed: here is a typical DC analysis, but there are many, both AC and DC.