Chemical reactions occur when two or more elements combine and form a new substance or when a substance is broken down into its seperate elements. Chemical reactions are everywhere. Bread rising is a chemical reaction. Fireworks going off is a chemical reaction. Fire burning is (well, I suppose you've already guessed this) a chemical reaction.
Reactions often change heat. An exothermic reaction, for example, is one where the product is hotter than what went into it. If the product is cooler than its reactants, then its called an enothermic reaction. There are many different sorts of chemical reactions. If an element combines with oxygen, the reaction is an oxidation reaction. If oxygen is removed from a substance, it is called a reduction reaction. If elements other than oxygen combine, then the substance formed is called a composition reaction. If a substance is broken down, it's called a decomposition reaction. Some reactions, like rust, occur very slowly. Others happen quickly, like fireworks.
In order for a reaction to take place, the reactants must all be in contact with each other. The size also matters. A cube of iron will rust more slowly than a sheet with the same amount of material, because the thin sheet has more surface area and the oxygen in the air can react with more iron particles. The concentration of the reactants also speeds up the reaction. The more molecules of each reactant, the more likely they are to come in contact and react. Heat can also increase the speed of the reaction, because it causes the heat causes the molecules to move more quickly. Adding a catalyst can also help. A catalyst speeds up the reaction, but is not used up.