Balloons are made of a thin sheet of a rubber called latex, which is made of long chain-like molecules tangled together.
The strands can be stretched, but when let go, the rubber returns to its original shape.
This type of material is called an elastomer.
When you push the needle slowly through, the strands move apart.
But if you push the needle through hard and fast, the network of strands will break and the air inside the rubber balloon will rush out and the balloon explodes.