To short-circuit a battery means that you connect the poles with a (short) piece of wire with negligible resistance. If you try it, you get even sparks, and your battery becomes hot, and flat in a very short time.
Now, internal resistance: When you connect something, for example a lamp to the battery, the current flows from one pole af the battery through the load (lamp) to the other pole and then through the battery to the first pole again, making a closed loop. But the battery itself has resistance. The electrodes themselves have, and there is some electrolyte material between them, and also some other material that absorbs gases, all of them have resistance. So we imagine a real battery as an ideal voltage source connected in series with a resistor Ri - the internal resistance of the battery. This internal resistance has to be taken into account if you calculate current. When you load the battery with a resistor R, R and Ri are connected in series, so I=E/(R+Ri). When the battery is short-circuited, R=0.
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