Hi Mena,
Boiling comes from bubbles on the plates. The bubbles are a "non conductor" and prevent that area of the plate from charging, that is until they become large enough to "break free" and float to the surface.
Really it is electrolysis (i.e. hydrogen at one plate and oxygen at the other). We just call it boiling because if you do it long enough the bubbles are pretty violent. The true boiling point of 100% sulpheric acid is 337 C (but of course we are dealing with a much weaker solution, so the boiling point is a bit over 100 C {212 F}).
Take a glass of water and put two "electrodes" in it. Connect it to a DC voltage source (a battery perchance?) with sufficient amperage. Watch what happens as the voltage is increased.