May I make a contribution to this discussion. Studio potters and hobby potters such as myself use kilns that are either heated electrically or are fuel-burning. Fuel-burning kilns either burn wood, or more commonly, gas, especially the small ones used by hobby potters. When firing electric kilns, the kiln atmosphere is always constant (air) and there is always plenty of oxygen available. But with fuel-burning kilns, the kiln atmosphere is potentially much more variable, ranging from an excess of oxygen (commonly called an oxidising atmosphere by potters) through to a deficiency of oxygen (commonly called a reducing atmosphere). The latter is achieved by limiting the amount of air that can enter the kiln so that there is insufficient to combust fully the fuel.
Firing a kiln 'in reduction' offers the studio potter a much wider and more interesting range of glaze colours and surface textures compared with firing in an electric kiln in oxidation. For example, soft greens can be obtained in reduction with iron in the glaze, compared with yellows and browns in oxidation, and copper can produce a spectacular rich blood red under reducing conditions. The chinese potters of antiquity used reduction firing to achieve such colours. Arabian lustre glazes are also made in a heavily reducing atmosphere. A potter with a fuel-burning kiln who only fired in oxidation might just as well use an electric kiln and save himself a lot of hassle.
As I said above, firing in reduction is achieved by limiting the amount of air entering the kiln so that the fuel is not fully burnt. Instead of the off-gas containing simply nitrogen, carbon dioxide and water vapour, hydrogen and carbon monoxide are also present.
For example burning propane in oxidation:
C3H8 + 8O2 ----> 3CO2 + 4H2O + 3O2
(I have deliberately included more oxygen than required to combust the propane, to show some in the off-gas. I have not shown the nitrogen)
In reduction:
2C3H8 + 6O2 ---> CO + 5CO2 + H2 + H2O
This is just one of an infinite number of equations that could be written, depending on the relative proportions of air and propane being used. Again, I have omitted the nitrogen.
But there are other reactions that take place:
CO2 + H2 CO + H2O
Note the double-headed arrow in the equation. This means the reaction can go either way, depending on conditions. If there is excess water vapour the reaction will go from right to left and the CO will take oxygen from the water to give CO2 and hydrogen. With excess CO2 present, the reaction goes the other way and hydrogen will be oxidised to water and the CO2 reduced to CO. At any one set of gas concentrations and temperature, there will be an equilibrium, and all four gases will be present together.
Another reaction is CO + H2 C + H2O
This is the 'water gas' reaction of old fashioned gas-works. Steam was injected into red-hot coke and hydrogen and CO were produced. In the presence of plenty of steam and the correct temperature, the reaction goes from right to left and coke (carbon) is converted to CO and H2. But if there's only a small amount of steam and an excess either of hydrogen or CO, the reaction goes from left to right and carbon (i.e. soot) is formed. IIRC, carbon black is made utilising this reaction, the CO and H2 being derived from burning propane in a gross deficiency of air.
So what takes place inside a pottery kiln is a complicated balance. Unburnt gas, oxygen, hydrogen, carbon monoxide, carbon dioxide, soot, water vapour and nitrogen are all present in equilibrium, the amounts depending on the exact conditions (a competent chemist can calculate the composition using thermodynamic data. There are computer programs for doing it). The potter adjusts the relative amounts of air and gas to give him enough combustion to raise the kiln temperature and prevent the formation of soot, but to have a slight deficiency of air to give a little CO and H2 in the kiln atmosphere and get the glaze effects he wants. This is usually achieved by adjusting the amount of secondary air entering the kiln. I don't know about studio pottery kilns, but the atmospheres in kilns of the big commercial tableware manufactures who fire in reduction typically contain a few percent (say up to 5%) of CO and H2.
A potter doesn't usually put his kiln into a reducing condition until it has reached say 900 - 1000C (although Arabian lustres are done at a lower temperature). At these temperatures the off-gas from the kiln emerging through the exhaust vent immediately ignites when it meets the air, resulting in a blue flame at the vent. Suppliers of gas kilns always give instructions that they should be operated under a hood with good ventilation. There is no danger of explosion, because as Andy Dingley explained, to get an explosion you need to create a mixture of a combustible gas with oxygen, and _then_ ignite it. In a pottery kiln the source of ignition is there all the time and an explosive mixture never gets a chance to build up. All gas kilns are fitted with flame failure devices, just like any other gas appliance.
Firing a gas kiln in reduction requires knowledge and experience of both the potting/firing processes and the appropriate hazards and safety precautions. While I wouldn't claim that no potter ever gets it wrong, I suspect that serious accidents are rare.