TL;DR Superheated products of burning in the state of plasma - essentially, an ionized gas.
Long answer:
Boring part on what causes the fire, you may skip it but it provides context
As is widely known, oxygen is the second most powerful elemental oxidizer in existence, second only to fluorine. Our atmosphere contains something like 21% of it in the form of oxygen molecules, and nearly everything it could oxidize at our normal conditions it already did - that’s how we got rocks, water and a lot of other good things. We also use it to oxidize our food - for us, this is just breathing, but really it’s a complex set of reactions meant to essentially burn our food at low temperature, without a flame.
However, one of the simplest things that can be changed to make oxygen oxidize something else is temperature. Elevated temperatures lead to the weakening of the bonds between atoms in the molecule, making them more readily available for a chemical reaction. At a certain threshold called activation energy, the reaction (in this case rapid oxidizing, i.e. burning) starts to occur. From here on out, the heat provided by reaction is enough to heat the rest of material up to the energy required for reaction, and it becomes self-sustaining, heating further and further. The further the reaction heats up, though, the more heat it emits to the environment, and at some point, different for each fuel type and external conditions, heating and cooling of the reaction equalize at a certain temperature - typically about 600-1000°C (1100-1800°F) for wood, 2000°C (3600°F) for natural gas, etc.
Normally, when a chemical reaction occurs, bonds get so weak that atoms can leave the molecule and reconfigure in a different way - they don’t stay in this separate state for any significant time, however, and the outcome is always two molecules with a different configuration of atoms. This is what happens inside our body in long chains of various reactions that involve oxygen. The end goal here is to extract as much energy as possible by putting electrons inside atoms in the most energy-efficient position, but that’s a topic for another time.
The thing is, fire works a bit differently.
Now the part actually about the fire
At such temperatures at which you see the flame, materials in the fuel don’t just swap atoms - they straight up break into free floating ions, or charged atoms, not bound to anything. They are so energized they rip chemical bonds apart. This state of matter is known as plasma, and it is very similar to gas, except gas consists of normal molecules and plasma is too hot to have that. So, in layman terms, you can see the flame as hot gas, though it wouldn’t be exactly correct.
Those ions then recombine into regular molecules, attempting to take the most energy-efficient configuration, and are moved out of the flame by the currents of air that itself gets expanded on heating. The products of this process are primarily carbon dioxide and water, as they are the most stable, energy-efficient bonds of carbon and hydrogen with oxygen, respectively.
As per why it glows - this is the property of its temperature. In fact, every object in the Universe that is above absolute zero temperature (0 degrees Kelvin, the lowest temperature there can be, signifying full stop in motion of any particles) emits electromagnetic radiation - that’s how thermal cameras work, they just see what we don’t. The interactions of protons and electrons between particles form paired electric and magnetic fields. These fields radiate photons, and at the temperatures above about 500°C (950°F) the emitted electromagnetic radiation begins taking form of visible light. Due to the amounts of heated matter and the energies involved in the process, we see fire as a very bright light.
TL;DR Superheated products of burning in the state of plasma - essentially, an ionized gas.
Long answer:
Boring part on what causes the fire, you may skip it but it provides context
As is widely known, oxygen is the second most powerful elemental oxidizer in existence, second only to fluorine. Our atmosphere contains something like 21% of it in the form of oxygen molecules, and nearly everything it could oxidize at our normal conditions it already did - that’s how we got rocks, water and a lot of other good things. We also use it to oxidize our food - for us, this is just breathing, but really it’s a complex set of reactions meant to essentially burn our food at low temperature, without a flame.
However, one of the simplest things that can be changed to make oxygen oxidize something else is temperature. Elevated temperatures lead to the weakening of the bonds between atoms in the molecule, making them more readily available for a chemical reaction. At a certain threshold called activation energy, the reaction (in this case rapid oxidizing, i.e. burning) starts to occur. From here on out, the heat provided by reaction is enough to heat the rest of material up to the energy required for reaction, and it becomes self-sustaining, heating further and further. The further the reaction heats up, though, the more heat it emits to the environment, and at some point, different for each fuel type and external conditions, heating and cooling of the reaction equalize at a certain temperature - typically about 600-1000°C (1100-1800°F) for wood, 2000°C (3600°F) for natural gas, etc.
Normally, when a chemical reaction occurs, bonds get so weak that atoms can leave the molecule and reconfigure in a different way - they don’t stay in this separate state for any significant time, however, and the outcome is always two molecules with a different configuration of atoms. This is what happens inside our body in long chains of various reactions that involve oxygen. The end goal here is to extract as much energy as possible by putting electrons inside atoms in the most energy-efficient position, but that’s a topic for another time.
The thing is, fire works a bit differently.
Now the part actually about the fire
At such temperatures at which you see the flame, materials in the fuel don’t just swap atoms - they straight up break into free floating ions, or charged atoms, not bound to anything. They are so energized they rip chemical bonds apart. This state of matter is known as plasma, and it is very similar to gas, except gas consists of normal molecules and plasma is too hot to have that. So, in layman terms, you can see the flame as hot gas, though it wouldn’t be exactly correct.
Those ions then recombine into regular molecules, attempting to take the most energy-efficient configuration, and are moved out of the flame by the currents of air that itself gets expanded on heating. The products of this process are primarily carbon dioxide and water, as they are the most stable, energy-efficient bonds of carbon and hydrogen with oxygen, respectively.
As per why it glows - this is the property of its temperature. In fact, every object in the Universe that is above absolute zero temperature (0 degrees Kelvin, the lowest temperature there can be, signifying full stop in motion of any particles) emits electromagnetic radiation - that’s how thermal cameras work, they just see what we don’t. The interactions of protons and electrons between particles form paired electric and magnetic fields. These fields radiate photons, and at the temperatures above about 500°C (950°F) the emitted electromagnetic radiation begins taking form of visible light. Due to the amounts of heated matter and the energies involved in the process, we see fire as a very bright light.
That’s it, in the nutshell :)