I was just wondering, whenever I visit any site it says pump the brake pedal three times then keep pressing it, what is the actual benefit of pumping it? And why not just press down the brake pedal and then open the bleeder screw without pumping?
You need to have positive pressure in the brake lines to get rid of any air; the pumping ensures you've built up enough pressure. And if the other sites you've read didn't mention it, you repeat the process (pump, hold, loosen bleeder valve while maintaining pressure on the pedal, close bleeder valve) until a solid stream of brake fluid comes out; that is the sign all the air is gone. And you can definitely tell the difference by the sound of the fluid coming out.