Internal resistance is the resistance within a battery, or other voltage sources, that causes a drop in the source voltage when there is a current.
Real batteries are constructed from materials which possess non-zero resistivities. It follows that real batteries are not just pure voltage sources. They also possess internal resistances. Incidentally, a pure voltage source is usually referred to as an emf (which stands for electromotive force). A battery can be modeled as an emf ε connected in series with a resistor γ, which represents its internal resistance.
It follows that if we short-circuit a battery, by connecting its positive and negative terminals together using a conducting wire of negligible resistance, the current drawn from the battery is limited by its internal resistance. In fact, in this case, the current is equal to the maximum possible current I. The effect of internal resistance will come into picture when the current starts flowing in the circuit because the internal resistance will also add to the resistance of the circuit.