First, take note that in your scheme the cap shows the wrong polarity! The plus pole must be connected to +5V, like shown here:

 
------------------        8.2k resistor 
            reset |-------\/\/\/\/\--------|||(gnd) 
                  |   | 
  microcontrlller |   | 
             side |   | 
-----------------   - | 
                     ===10uF 
                    + | 
                      | 
                     +5V 

This circuit works very simple: Immediately after power-up the cap is still uncharged and forces the reset input line to high potential. Afterwards, the cap becomes charged more and more via the 8k2 resistor and finally the potential at reset input line will show low potential. Means, as long as the cap isn't charged, concretely spoken during a time period of about R x C, the micro sees an active reset signal and is held in reset state to allow the built-in oscillator to fully start-up.

This RC-reset circuit is simple but disadvantageous. A fast power-up is needed to allow the cap to be uncharged immediately after power-up. This cannot be guaranteed always. Think of mains powered applications, for instance, where a soft transformer is unable to provide an immediate supply voltage. So, you will mostly find it in battery powered toys, where the failing of reset doesn't harm and can be simply "cured" by the toy turning-off and -on again.

Another disadvantage is, that there's no reset at all, when Vcc falls under nominal voltage due to a dip of mains voltage, for instance. So, when not just designing a toy you should use a proper reset chip, best with built-in watchdog, like MAX1232, for example.

Micros containing a flash code memory are highly susceptible against power-ups and -downs without proper reset signal. If there's no stable reset at power-up and -down, the code memory can be corrupted! So, flash micros should always have a proper reset circuit, even when only designing a toy...

Kai