What actually happen if we click the power button in iPhone? Are we turning it off?
Are putting iPhone on standby mode?
What mode are we putting iPhone in?
Can calls get in?

I noticed that musics from music video get turned off which sucks because I want to be able to put my iPhone on standby mode and keep listening to music.
When you press the sleep/wake button, you simply turn off the screen (and lock the device). Audio will still play when the screen is off, but video will stop. Everything else that the phone does will largely be unaffected. Background processes like navigation, audio playback, alarms, etc. will function like normal. Calls, text messages, and notifications will still come in.

Source
https://a248.e.akamai.net/7/248/51/20120908/manuals.info.apple.com/MANUALS/1000/MA1565/en_US/iphone_user_guide.pdf