How does Arduino know when to stop counting button presses?

Hi there.
It was was bothering me for a very long time how does Arduino or any other micro controller knows when to stop counting button presses?
For example when I press once light1 turns on/off, then twice light2 and so on.
What if I have only 3 lights and and I have pressed 3 times within 3 seconds and then after couple of minutes I want to turn off the light3 and I press 3 times again.
How does arduino know that it should be 3 presses rather than 6 (3 current and 3 past presses)?
Is there any way that you can define time for input and then reset the timer?

/*
  State change detection (edge detection)
 	
 Often, you don't need to know the state of a digital input all the time,
 but you just need to know when the input changes from one state to another.
 For example, you want to know when a button goes from OFF to ON.  This is called
 state change detection, or edge detection.
 
 This example shows how to detect when a button or button changes from off to on
 and on to off.
 	
 The circuit:
 * pushbutton attached to pin 2 from +5V
 * 10K resistor attached to pin 2 from ground
 * LED attached from pin 13 to ground (or use the built-in LED on
   most Arduino boards)
 
 created  27 Sep 2005
 modified 30 Aug 2011
 by Tom Igoe

This example code is in the public domain.
 	
 http://arduino.cc/en/Tutorial/ButtonStateChange
 
 */

// this constant won't change:
const int  buttonPin = 2;    // the pin that the pushbutton is attached to
const int ledPin = 13;       // the pin that the LED is attached to

// Variables will change:
int buttonPushCounter = 0;   // counter for the number of button presses
int buttonState = 0;         // current state of the button
int lastButtonState = 0;     // previous state of the button

void setup() {
  // initialize the button pin as a input:
  pinMode(buttonPin, INPUT);
  // initialize the LED as an output:
  pinMode(ledPin, OUTPUT);
  // initialize serial communication:
  Serial.begin(9600);
}


void loop() {
  // read the pushbutton input pin:
  buttonState = digitalRead(buttonPin);

  // compare the buttonState to its previous state
  if (buttonState != lastButtonState) {
    // if the state has changed, increment the counter
    if (buttonState == HIGH) {
      // if the current state is HIGH then the button
      // wend from off to on:
      buttonPushCounter++;
      Serial.println("on");
      Serial.print("number of button pushes:  ");
      Serial.println(buttonPushCounter);
    } 
    else {
      // if the current state is LOW then the button
      // wend from on to off:
      Serial.println("off"); 
    }
  }
  // save the current state as the last state, 
  //for next time through the loop
  lastButtonState = buttonState;

  
  // turns on the LED every four button pushes by 
  // checking the modulo of the button push counter.
  // the modulo function gives you the remainder of 
  // the division of two numbers:
  if (buttonPushCounter % 4 == 0) {
    digitalWrite(ledPin, HIGH);
  } else {
   digitalWrite(ledPin, LOW);
  }
  
}

if (buttonPushCounter % 4 == 0) {

The % is the moduls operation, look it up.
It gives you the remainder or a division by four. The counter will count up to just over 16000 before it wraps round again to zero but your code just looks at the remander of dividing by four.

How does arduino know that it should be 3 presses rather than 6 (3 current and 3 past presses)?

It doesn't, unless you tell it to reset to 0 when it gets to, or past, 4.

Is there any way that you can define time for input

As in, the switch must be pressed n times in x seconds? You could do that. Record the current time (using millis()) when the event of interest occurs (whatever defines the start of x seconds). Then, periodically (every pass through loop()), see if now minus then exceeds x seconds and the number of switch presses is less than n.

and then reset the timer?

Like you reset your watch all the time? No. Don't even go there.