Nib asked, and Nib — askNib's tutor — drew the answer live at a whiteboard. This is the spoken transcript; enable JavaScript to watch it drawn.
how does a battery cell work
A battery does not store electricity. There is no tank of electrons inside. What it stores is chemistry: two materials that are itching to react with each other.
Take the classic pair, zinc and copper. Zinc lets go of electrons easily, copper grabs them. That difference is a hill of one point one oh volts, and electrons want to roll down it.
Now build it. A zinc strip in zinc sulfate on the left, a copper strip in copper sulfate on the right: two half cells, kept apart so electrons cannot hop straight across.
On the zinc side, each zinc atom lets go of two electrons and dissolves as an ion. The electrons have only one way out, the wire, so they race to the copper.
At the copper, the arriving electrons turn copper ions into solid metal. A salt bridge lets ions drift across, keeping both sides balanced so the current keeps flowing.
So a cell is a hill for electrons with a wire for the slide. When the zinc is used up the hill is flat and the battery is dead. An A A battery swaps in manganese dioxide for one point five volts.
Next time a remote dies, remember: nothing leaked out. The chemistry just ran out of road.