What is cold pressed method to extract Juice?
Cold pressing is as the name implies, to press(instead of blending) juice from a fruit while minimizing heat generation. You can buy these cold pressing juicers from the market as they're quite common nowadays.

Cold pressers from the market will likely have a rotating core (think drill bit) fixed in a tube structure. Drop your fruit from the top, and juice comes out after it gets pressed by the slowly rotating core.

The need for cold pressing juices likely came about when people thought that the traditional style of juice extraction via a blender/juicer subjects the mixture to high shearing/centrifugal forces which introduces heat and oxygen, which degrades the nutrients and vitamins in the juice. On the other hand, cold pressing purportedly negates these effects by "gently" treating the fruit. (think your cold pressed olive oil, coconut oil etc.).

Personal opinion: Since you essentially discard the fibrous parts of the fruit (that has a ton of benefits!) and consume the sugary mixture, your body will absorb a lot of sugar in a short time. Have a whole apple instead! :) 

Slight addition:

For the heat generated by a blender, you may refer to this: 
Experiment on waste heat in a blender. Over 3 minutes time, 9.4 degC rise was achieved in 200mL of water with a 350W blender. Of course, with fruits in the mixture the figure might vary slightly so take it with a grain of salt.

Sources:

(1) https://www.wired.com/2015/04/nobody-can-prove-cold-pressed-juice-better/

(2) http://www.ctvnews.ca/health/fact-check-are-cold-pressed-juices-worth-the-hype-1.2926121

(3) My mum bought a cold pressed juicer