Why won't my iPhone 5s charge?

Yesterday evening my phone began having problems charging. It would stop, but then start again. I waved it off as nothing, thinking maybe the charger came out of the wall socket. I plugged my phone into my computer and it kept doing it again. Finally, it wouldn't charge in the car, but my car charger has problems so I waited until I went to my friends house. Even then, it wouldn't charge for awhile. We tried different sockets and it finally started charging.

My phone has just died and I have plugged it into different sockets and usb ports but to avail. Why won't my charge phone and how