Fire damage is one of the five Damage Types. It is reduced by Fire Resistance. Fire Hits inflict Flammability based on how much Fire damage is dealt, which provides a chance to Ignite.

Ailments are a family of common Debuffs associated with specific damage types. The list of Ailments is: Bleeding, Ignite, Chill, Freeze, Shock, Electrocute, and Poison.

Ailments that deal damage are Bleeding, Ignite, and Poison.

Elemental Ailments are Ignite, Chill, Freeze, Shock, and Electrocute.

Flammability is a Debuff that provides the chance for Hits to Ignite the target. It is not itself an Ailment, but is closely associated with Ignite, which is.

Fire damage from Hits Contributes to the Magnitude of Flammability, so Hits that deal more Fire damage will Ignite more often.
The base Magnitude of Flammability is 1% chance to Ignite the target for every 5% of the target's Ailment Threshold dealt as Fire damage. Flammability from a Hit is applied before that hit checks whether it should Ignite the target, and so will affect that chance for that Hit to Ignite.

Since chance for Hits to Ignite comes from Flammability on the target, modifiers which increase the chance to inflict Ailments will increase the Magnitude of Flammability inflicted.

Effects which do not Hit targets, but Ignite as if they had, such as Ignited Ground, also inflict Flammability, but do not roll a random chance to Ignite. Such effects will onlyIgnite once the total Flammability on the target reaches 50%.

Multiple instances of Flammability stack, raising the chance for Hits to Ignite the target up to 100%. Each instance of Flammability has its own independent duration, lasting 8 seconds by default.

Burning damage is any Fire damage dealt over time, including things like Ignite.

Ignited Ground repeatedly inflicts Flammability on enemies as long as they are standing on it, Igniting them when it reaches 100%. By default, Ignited Ground lasts for 4 seconds and has a radius of 2 metres unless otherwise specified.

Ignite that has been Aggravated deals 100% extra damage.

Once an Ignite has been Aggravated, it will remain Aggravated until its duration expires.

Just like Bleeding, each Ignite Debuff can be Aggravated, or not, independently of others on the target.

Damage can be converted from one type to another. This causes it to deal the new damage type, scale with modifiers to the new damage type, and no longer scale with modifiers to the old damage type.

For example, Fire damage converted to Lightning now scales with Lightning damage modifiers and causes Shock, but no longer scales with Fire damage modifiers or causes Ignite.

Conversion is a two step process. Conversion inherent to Skills occurs first, then Conversion from all other sources. Damage over time cannot be converted.

Enemies covered in Oil have their movement speed Slowed, are inflicted with Fire Exposure and have 200% more Magnitude of Flammability inflicted on them.

Ignited Ground or Detonator Skills will Ignite Oil-covered enemies. This removes the Oil, but the Exposure will remain for the duration of that Ignite.

Enemies standing in Oil Ground have their movement speed Slowed and are inflicted with Exposure.

Ignited enemies, Ignited Ground, or Detonator Skills that touch the Oil cause it to catch fire, Igniting enemies instead of Slowing them, but still inflicting the Exposure.

Chilling Enemies grants 1 Unbound Fury, Shocking or Igniting Enemies grants 2 Unbound Fury and Freezing or Electrocuting Enemies grants 6 Unbound Fury.

By default, specific Ailments are calculated based on only specific damage types, such as only the Fire damage of a Hit mattering when inflicting Ignite.

Allowing another damage type to contribute to an Ailment means that all damage of the relevant types is summed when performing calculations for that Ailment.

For Ailments that use Hit damage to determine Ailment chance or buildup, this means that the damage type becomes capable of inflicting that Ailment. For Ailments that only use Hit damage to determine Ailment Magnitude (i.e. Bleeding and Poison), you still need a way to apply those Ailments (e.g. a source of Bleeding or Poison chance).

Targets affected by a Spectral Fire Debuff do not take damage from Ignite. Instead that damage feeds the Spectral Fire. When the Spectral Fire Debuff expires or the target dies, the Spectral Fire explodes, dealing all the damage it has absorbed to all enemies within 1.8m, including the affected target.

Fire Spells Convert 100% of Fire Damage to Chaos Damage
Chaos Damage from Fire Spells Contributes to Flammability and Ignite Magnitudes
Ignite inflicted with Fire Spells deals Chaos Damage instead of Fire Damage

While affected by Unravelling, your Chaos Damage randomly either also contributes to Freeze buildup, Flammability and Ignite Magnitudes, or Shock chance - changing which it contributes to every two seconds.