You use it when something makes your life more difficult. "I had to take the exam at 7:00 in the morning. What a pain in the neck. "She's always complaining about something to me. She's becoming a real pain in the neck." "I hate filling out all these forms just to open an account. This is a royal pain in the neck."

It means something that is a bother or an annoyance. You will be just as likely to hear 'pain in the ass', which is a little more emphatic because it's a little more rude. I prefer it. :D

It's something or someone who is annoying or bothersome. "Applying for that job is a real pain in the neck because there are so many pages to fill out."

The term "Pain in the neck." comes from the physical results of a stressful situations. When you are tense, stressed or worried about something the muscles in your shoulders and neck become tense and start hurting. So when you are in a stressful situation you say "It's a pain in my neck" (even if it isn't) to explain just how bad a situation it it. Those are just my thoughts, hope it helps.