What exactly is jailbreaking?

So, I want to know what exactly is jailbreaking, what are the risks of doing that to your iPod/iPhone/iPad, and can it be undone? I'm kind of scared to do this, because it sounds illegal, and I'm afraid I might break my iPad. Also, how do you jailbreak, and what can you do once it's jailbroken?

How to get my music transferred to my new iPhone?

I got a new iPhone today. I need to know how to sync the itunes to my new phone. When i went on my itunes the sync button wouldn't pop up. I don't have icloud or whatever it's called, and I also don't have my old iphone. So if there's a way to transfer the music please share!