Oxygen comprises about 20% of the air we breathe (and even the air we don't breathe). At this concentration, many things react with oxygen in combustion reactions, often releasing heat and light energy. However, many of these combustion reactions occur much more readily in an atmosphere of pure oxygen.
Organic compounds (compounds containing carbon) react with oxygen to produce carbon dioxide and water:
Organic compound + O2 ——> CO2(g) + H2O(g)
Wood, of course, burns very well in air, producing a lot of heat and light (and smoke). The reddish-yellow color of the flame is the result of the inability of the solid wood to mix very well with the gaseous oxygen in the atmosphere; as a result, some elemental carbon is also produced, which glows with a reddish-yellow color. In the presence of pure oxygen, wood burns even more quickly.
In the following demonstration, a wood splint is lit in a Bunsen burner, which is then thrust into a jar containing pure oxygen. The flame flares up even more brightly, and the splint burns much more rapidly than it would in normal air:
Video Clip: REAL, 2.68 MB
!!! Hazards !!!
Setting anything on fire involves risks, of course. Handle the splint with a pair of tongs, and keep other inflammables away.
John Emsley, The Elements, 3rd ed. Oxford, Clarendon Press, 1998, p. 148-149.
David L. Heiserman, Exploring Chemical Elements and their Compounds. New York: TAB Books, 1992, p. 32-36.