A Manifestation of ones ki, In this case in a fireball-like form. Exhibited in the street fighter series by characters such as ken,ryu,sakura,akuma,dan(to a lesser extent) and so on. In the true street fighter canon,it is said that the temperature can be anywhere from a "cold bath" "to a hot bath" in which the heat of the hadouken plays a small part in the damage aspect. it is the actual force of the energy that does that damage. So it feels like a "super hard punch".
Sakura's hadouken is the temperature of a tepid bath.