The software will charge the capacitor and the resistor will discharge it.
When GPIO14 is low, the IC will wake up from auto light sleep and respond to any pending request that the WiFi router has in queue for it, and also can do some other stuff to send requests.
You also have the option to externally pull GPIO14 low and start the process for lower latency.
I usually use a 33pF capacitor and 1MOhm resistor which causes the IC to wake about every 5 seconds.
So when i send an HTTP request with a browser, it can pause for up to 5 seconds before it gets a response.
I think i have more detail on my repository..
https://github.com/leon-v/ESP8266-NONOS-SDK-2.0-Low-Power-WiFi-Node
http://www.eevblog.com/forum/projects/real-time-low-power-(10mw)-esp8266-expirments/msg1211703/#msg1211703