Heat plus oxygen makes stuff oxidise.

Oxidising gives off heat.

Enough heat makes stuff vaporise.

Vapour oxidises faster and hotter.

Even more heat makes vapour glow.

Flames are glowing vapour.

The shape of flames are based on heat making vapour rise, and taking it away from the main heat source until it stops glowing.

It’s another state of matter. You know gas, liquid, solid, right? Well, there’s actually a shitload of those, not just three. The fourth they’ll teach is called plasma, and it’s when the atom has gotten busted up into floating electrons and nuclei. Your candle flame is a plasma.

The light from a lightning bolt is from glowing plasma too. So is the surface of the sun for that matter.

edit: Oh, and fire is caused when you ram oxygen atoms into the atoms of something burnable so hard that they join together. This makes a lot of heat and gas fly off, which combine into the plasma. Then this just happens a whole bunch over and over.