A half reaction equation is used to show either the oxidation or the reduction process in the equation.
For the given example, hydrochloric acid dissociates as `HCl -> H^+ + Cl^-` .
The reduction half reaction equation is `2H^+ + 2e^-1-> H_2(g)` .
The `Cl^-` ion combines with the positive ion of the chemical that the acid is reacting with and forms a compound with it. For example, if HCl reacts with sodium metal.
`HCl -> H^+ + Cl^-`
`2H^+ + 2e^-1-> H_2(g)`
and `Na^+ + Cl^(-) -> NaCl`
The Cl in HCl takes part in the other half of the reaction, it is not shown in this half reaction equation as that does not have any relevance here.