The head of a match uses antimony trisulfide for fuel. Potassium chlorate helps that fuel burn and is basically the key to ignition, while ammonium phosphate prevents the match from smoking too much when it's extinguished. Wax helps the flame travel down the matchstick and glue holds all the stuff together. The dye-- well, that just makes it look pretty. On the striking surface, there's powdered glass for friction and red phosphorus to ignite the flame.
Now, the fun stuff-- striking a match against the powdered glass on the matchbox creates friction. Heat from this friction converts the red phosphorus into white phosphorus. That white phosphorus is extremely volatile and reacts with oxygen in the air, causing it to ignite. All this heat ignites the potassium chlorate, creating the flame you see here.
Oxidizers, like potassium chlorate, help fuels burn by giving them more oxygen. This oxygen combines with antimony trisulfide to produce a long-lasting flame so you have enough time to light a candle. The whole thing is coated with paraffin wax, which helps the flame travel down the match. Just don't burn the house down.
As antimony oxidizes, sulfur oxides form, creating that burnt-match scent. The smoke you're seeing is actually tiny unburned particles resulting from an incomplete combustion. Individually, they're a little bit too small to see but grouped together, they form smoke. There's also some water vapor in there.
By the way, all the stuff that we're explaining in 90 seconds, it all happens within tenths of a second. Chemistry's fast.
