Sorry to sound like a total 'n00b' but what's the deal with amps? How do they make sound quality better and is it a huge difference without it?

Is the Audio-Technica ATH-M50S an uncomfortable headphone to use for extended lengths of times? How can you tell this is a characteristic of the headphone? Does anyone have personal experience with it?

I'm interested in buying some good quality headphones for around the $100 to $150 price range. I've been searching and have found the Audio-Technica ATH-M50S to seem to be pretty good. My question is - What's the best headphones I can buy for my price range?   Note: I mainly going to use it...