In order to avoid the danger of accidentally spreading a fire, many campers pour water on the embers or cover them in dirt.
It continues to stay hot and does not lose its thermal energy quickly because combustion is still happening at a low level.
Once the embers are completely 'burned through', the remains are oxidized minerals like carbon, calcium and phosphorus.
Because embers are typically burnt leaves and thus small and lightweight, they can easily become airborne.
[1] A number of practical measures can be undertaken by homeowners to reduce the consequences of such an "ember attack" that bombards especially wooden structures and starts property fires.