Why #"HCl"# is an acid can be explained on basis of many theories, like Arrhenius theory, Bronsted-Lowry acid base theory, and Lewis acid-base theory.
According to Arrhenius theory, a compound which when dissolved in water dissociates and furnishes #"H"^(+)# ions is an Arrhenius acid.
According to Bronsted-Lowry theory of conjugated acid-base pairs, the #"H"_3"O"^(+)# forms a conjugate base which is water (weakly basic). So #"HCl"# is a Bronsted acid because it donated an #"H"^(+)# to water.
According to Lewis Theory, any compound which can accept lone pair of electrons from a donor atom/molecule/group is an acid.
#"H"^(+)# being a cation easily accepts lone pair of electrons.
So #"HCl"# dissolved in water forms a Lewis acid.
Therefore, #"HCl"# is a strong acid as it readily and easily dissociates in water and furnishes #"H"^(+)# ions. The dissociation is 99.9%, which makes it a strong acid.
