keeping my hand near the arduino board affects my output

i made one analog pin(a3) as input and one PWM pin(9) as output. i connected the PWM pin(9) with an LED. when i moved my finger across the analog pin, the led glows brightly. but i din't connect anything in the analog pin(a3). why this is happening?
here is my code:

int ledPin = 9; // LED connected to digital pin 9
int analogPin = 3; // potentiometer connected to analog pin 3
int val = 0; // variable to store the read value

void setup()
pinMode(ledPin, OUTPUT); // sets the pin as output

void loop()
val = analogRead(analogPin); // read the input pin
analogWrite(ledPin, val / 4); // analogRead values go from 0 to 1023, analogWrite values from 0 to 255

why this is happening

Because your input is floating.