Purpose of 1 microfarad capacitor in IR receiver circuit
...  the datasheet is too advanced for me. Is there a beginner way to understand ...


Sure. Let's do it in stages.

Modulated waveform



Figure 1. Infrared modulated and demodulated signals.


Remote control signals are transmitted as a series of pulses. If you look at the LED on your TV remote using your camera phone you can see the irregular flicker as you press the remote buttons. The remote control codes are sent at a relatively low speed of up to 1200 bits/s according to the datasheet.
Each pulse for one bit will, in turn, be made of a burst of high frequency pulses. The top of the datasheet shows that the chips are made in versions from 30 kHz to 40 kHz. Having rapidly changing levels like this helps the receiver discriminate between background infrared from other sources. Effectively the receiver is looking for a fast AC signal and ignores anything else.




Figure 2. The innards of the TSOP demodulator.


The TSOP chips make decoding the signals easy because they demodulate the output and restore the low frequency signal. See the output signal of Figure 1.
The demodulated signal is used to drive the output transistor. Note that this has a pull-up resistor which normally holds the output high. When the transistor turns on the output is pulled low.








simulate this circuit &ndash; Schematic created using CircuitLab

Figure 3. The output of the sensor.


If the transistor, Q0, is off (no signal received) the output is pulled high by R-pull-up. This charges up C1 to V+.
When the receiver turns on Q0 it discharges the capacitor to 0 V. 
When Q0 turns off C1 starts to charge up via R-pull-up. The time taken to charge is given by \$ \tau = RC = 100k \times 1 \mu = 0.1 \ \mathrm s \$. As a result the output will stay low for about 0.1 s after the last received pulse.



  But how does the capacitor know when to release the charges it holds to IC's pin 13? Does the capacitor wait for the burst of pulses to finish before releasing the charges to the IC's pin 13?


Yes. As explained above the pull-up resistor is always trying to charge up C1 but every pulse from Q0 discharges it again. The time constant is 0.1 s so it will charge again about 0.1 s after the last pulse detected.




  I think it is getting clearer especially the 0.1 s. But how does the Pin 14 of IC count all the pulses of a series as 1 pulse if the capacitor discharges and charges many times if I press one button in a TV remote control?


That's easy. 


Every time the TSOP receives a pulse the capacitor is discharged and will take 100 ms to recharge.
The TSOP chip is demodulating the received signal into nice square pulses. We don't know, but let's say they're coming in at half the maximum rate the TSOP can handle = 1200/2 = 600 pulses/s. So, one pulse = 1/600 s = 1.7 ms.
So, from the above we can see that while the button is pressed on the remote control the capacitor will be discharged to zero again every 1.7 ms. It's only when the button has been released for > 100 ms that the capacitor can recharge.
The result is that the counter gets one pulse for each press of the button provided there is at least 100 ms between presses.