Most metals will react with oxygen; known as oxidization. You can see this when rust builds up on iron that has been exposed. However, for an explosion, a rapid release of energy, you want this oxidization process to happen quickly. So you can either ground up the metal you are using, blast it into the are by firing a rocket, and the increased surface area of the metal particles will result in rapid oxidization and pretty colors.
Another method is to use gunpowder, made from coal or carbon which contain a lot of oxygen atoms. When heated the chemical bonds become unstable, releasing oxygen for the metals to oxidize with, which generates heat, releasing more oxygen etc. Obviously this is happening very quickly.
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