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.
