Why doesn't my Samsung cable charge?
The Power which your Phone consumes outway the Power a USB Port can supply.
This problem is often faced when using an Powerbank.  

Cause could be an old Battery which lifetime is coming to a close, but thats anyones guess.
I would buy myself a charger that goes in to the Wall socket. Way more convinient.
For example, it would take 5h for my Nexus 5 to fully recharge from USB and only 2 hours from the wall Socket directly.