The issue is with Lithoum-Ion batteries (following the Samsung Galaxy failures).
There is no restriction on standard AAA, AA, C or D batteries, they can be transported in your checked luggage or in your carry-on. TSA does prefer that they are in their original packaging (versus loose) to reduce the risk of rubbing and shorting out.
You can also transport larger lithium batteries that are installed in a component (camera, strobe, torch, computer, etc) provided they are less than 100 watt-hours each. As long as they installed in a component, the component can be transported in either your checked luggage or your carry-on.
Spare lithium batteries less than 100 watt-hours can be transported in your carry-on luggage, but can not be in checked luggage. There is no restriction to the number of batteries you have in your carry-on, provided they are less than 100 watt-hours.
You can also carry up to two larger lithium batteries up to 160 watt-hours in your carry-on luggage. Nothing above 160 watt-hours is allowed onboard.