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DIVE INTO THE CHEMISTRY BEHIND IT ALL
Matches
There are two types of matches: safety matches and "strike anywhere" matches. Although safety matches can only occur when it strikes against a match box, the process on how fire is created is the same as a strike anywhere match. Match boxes are typically made of sand, powdered glass, and red phosphorous. A strike anywhere match can use anything solid to light it.
Type 1. Safety Matches
To create fire, a redox reaction must occur in which electrons are transferred from one chemical to another. A typical equation for lighting a match is

16KCl3 + 3P4S3 ---> 16KCl + 9SO2

The head of a safety match is made out of sulfur, glass powder, and an oxidizing agent--the most common being oxygen (however, there are other oxidizing agents, too). When the head of the match is struck against the match box, friction from the glass powder causes red phosphorus to turn into white phosphorous, catching fire in air. Oxygen gas is produced through redox reactions; that, with heat, causes the sulfur to burst into flame, resulting in the wood on the match to catch fire.
Type 2. "Strike Anywhere" Matches
Red phosphorous is the main agent for fire; safety matches are, well, safe, because one cannot simply strike the head of a match on any surface--only the match box, which contains phosphorus.

One can strike a "strike anywhere" match anywhere because the red phosphorus is no longer on the match box--it is now on the head of the match. Thus, striking this match on any rough surface (rocks, wood, etc.) will produce enough friction, heat, and oxygen gas to cause sulfur to burst into flame and light the match on fire. One can tell the difference between a safety match and a strike anywhere match because the safety match's head is only one color, whereas a strike anywhere match is two colors--one for phosphorous and the other for the oxidizing agent.
Why Red Phosphorous?
When matches were first discovered, white phosphorous was used to create fire; however, it later turned out to be very toxic and deadly. Highly reactive, this will produce damage to the body heavily, some of which including gastrointestinal irritation, liver damage, bony necrosis, and anemia.
Black Phosphorous is another form of phosphorous; however, this is the least reactive and can only turn into white phosphorous through extreme pressure.
Red Phosphorous is perfect for matches: it is stable at room temperature and can turn into white phosphorous through heat, sunlight, or friction. Not only is this used in matches, it is used in various explosives--including fireworks!