From first glance, I *assume* you either have a defective battery or a defective charging cable. Try using a different charging cable and/or wall plug. If that doesn't work, try a different wall socket. If that fails, take it to a nearby Apple Store to have them diagnose the problem for you.
I wonder if your phone is stuck. Try holding the home and power button at the same time for about 10-20 seconds and see if anything comes up on the screen
My view on phones not getting charged mostly lies with the battery being faulty or the charging port. I would get my iPhone fixed at a store personally if I knew my phone was spoiled in that way.