Once a proton is removed and is capable of forming a stable conjugate base then it is considered strong acid. For instance of HF and HCl being a strong acid, it could be explained by this; because once the proton is removed, the electronegativity of the halogen group stabilizes anionic conjugate base.
This type of stabilization is also used to describe acidity of carbonic acids and acidity of the protons on the alpha carbon of the carbonyl compounds.