The battery light on a car is just an idiot light and does not necessarily mean the battery is bad. More likely is a bad alternator. If you or a friend has a digital volt ohm meter set it to VDC (Volts DC) and put the meter on the battery terminals with the car running. If your alternator and voltage regulator (They are combined in newer cars) then the meter should read about 13.8 to 14.5 VDC. If it reads less have your alternator tested and/or replaced.
alternator or bad wires
If no light is on and no relay is stuck then the battery has a dead cell and needs replacing.
Something is on drawing power. Can be any light on the vehicle or a relay stuck.
Whether the key is on or not, you have a low battery and it might need replacing.
on my old 1.2 clio the battery light came on as there was fault with the alternator and it needed replacing. As far as i know the battery light comes on when the battery is not charging or there is a fault with the battery.
My check engine light came on because the terminals were not connected tightly. no. quite the contrary. if you have a "check engine" light on, disconnecting, or in this case replacing the battery will turn it off. you have a different problem.
If the light is still on then the problem was not the battery but was instead the alternator which is more than likely defective.
MAYBE IT COULD BE A BAD SENSOR. IF IT IS RUNNING GOOD I WOULD JUST IGNORE IT.
A dead cell within the battery itself will drain the battery. There is no fix for this except replacing the battery. You may also have something that is pulling power from the battery. Examples are under hood light, dome light, glove box, trunk, courtesy light, and any numbers of relays.
Only if something is wrong. Drive it to your local auto parts store and have them check the system. Most do it for free.
Clean both battery cables and check the connections on the alternator. If it continues, go to auto zone and have the alternator checked.
To indicate to you that it may need charging, replacing, or a loose connection.