If you have ever played with a Jack-in-the-Box then you know that it springs out of the box after you turn the little handle a while.  Well the reason it bursts out is because all the pressure builds up and since it has nowhere to go it pushes and pushes at the top to get out until the top pops up and the little man springs out of the box.  The Jack-in-the-box is just like fireworks, once the firework has been lit all the pressure builds up, the fire burns the wick and reaches the firework and all the contents inside the firework explode out it.  The content that makes the firework explode is the black gun powder which is located at the end of the firework where the wick is located.  This causes the gun powder to ignite and explode.