battery cell
A battery cell is a sealed chemical engine that stores energy in chemical bonds and releases it as a flow of electrons on demand. Picture two reactive materials kept apart, each desperate to swap electrons but only allowed to do so through an external wire: as the reaction proceeds, electrons stream out one terminal, through your circuit, and back into the other, while ions shuffle internally to keep the books balanced. A single AA cell delivers about 1.5 V; the 3.7 V of a phone cell or the 1.2 V of a rechargeable NiMH cell is set purely by the chemistry inside, not by its size.
Every cell has a positive electrode (cathode on discharge), a negative electrode (anode), and an electrolyte that ferries ions but blocks electrons, forcing them through the load. A 'battery' is really one or more cells in series or parallel — a 12 V car battery is six 2 V lead-acid cells stacked in series. Bigger cells hold more charge (more amp-hours) but the voltage stays fixed by chemistry, which is why you series cells for higher voltage and parallel them for more capacity.
Don't confuse a cell with a battery: strictly a 'battery' is a pack of cells, though everyday speech calls a single AA a 'battery' too.