Don’t Blow a Fuse
Without a properly designed fuse a firework could ignite too soon or too late causing damage and wrecking the show. A professional firework actually has 3 fuses:

Main Fuse - The main fuse lights two secondary fuses: a fast-acting side fuse that ignites the lift charge, and a time-delay fuse buried inside the shell that leads to the heart of the firework.
Fast Acting Side Fuse – when lit this fuse burns quickly and ignites the lift charge (black powder packed into the bottom of the shell). This propels the firework into the air.
Time Delay Fuse - As the shell flies through the air, the time-delay fuse continues to burn. By the time the shell nears its maximum height, the fuse has burned low enough to ignite the black powder in the first break (compartment). Coloured stars ignite in every direction. The fuse keeps burning. In a three-break firework, the middle break needs to ignite at the highest point in the shell's trajectory, the first break should blow a little before and the third break a little after. If the timing is off, the firework might detonate too close to the ground. Great care is used in designing the fuses and calculating their lengths.
There are two main types of fuses: slow-burning and fast-burning:
‘Black match’ is the most common type of slow-burning fuse. It consists of a string dipped in black powder (gunpowder). Black match burns at a rate of 2.5 cm/sec.

Burning black match. (http://www.pyrouniverse.com/)
The most commonly used fast-burning fuse is ‘quick match’. Quick match is simply black match that has been covered with a loose-fitting paper tube (known as pipe). When a regular black match fuse burns, the hot gas produced by the flame escapes into the air in every direction. When the fuse is put in a paper tube, however, the hot gases cannot escape, so they shoot forward, along the length of tube, at incredible speeds. Quick match burns at a rate of approximately 40 meters/sec.

Quick match: a bundle of black matches encased in a paper tube. (http://www.pyroworx.com/quick_match.htm)
Why use two different types of fuses? The different types of fuses are used to join several fireworks together. For instance a group of fireworks would be joined together with quick match, so that they light at nearly the same time. The quick match is linked to the main fuse, which consists of a single tail of black match to be used as a slow fuse for lighting. The main fuse allows for enough time to get away before the explosion. The main fuse is then connected to both the fast acting side fuse (composed of quick match), and the slower time delay fuse (made of black match).
The more recent fireworks shows use computers to fire their shows electrically from a firing booth. This is a safer method, as it does not require a person to light the fuse directly.