Look at some POTENTIAL ENERGY DIAGRAMS for chemical reactions. They represent the progress of a reaction with time. For a favourable reaction (one which releases energy) you will see a flat line, then a "hump" then a lower flat line. The hump represents the ACTIVATION ENERGY for the reaction. This is the energy needed to break up the molecules in the otherwise stable mixture. The molecule fragments are the ACTIVATED COMPLEX and they are now able to react. The flame from the match provides the initial heat for this and when the molecule fragments react they supply more heat to other molecules to keep the reaction going until all of the mixture is reacted.
Hydrogen and oxygen react to form carbon dioxide and water under certain conditions.
It is important to remember that all chemical reactions take place under specific conditions. If the conditions are right, the reaction becomes favorable. For example, some reactions take place only in a certain pH range or a certain temperature range. We typically see the combustion of methane and oxygen when energy is added in the form of heat. You have probably experienced this when you light a Bunsen burner. Friction from flint is typically the catalyst to this reaction.
Hope this helps!