When a metal reacts with an acid it liberates hydrogen gas. In the activity series of metals, the metals which are above hydrogen can displace it, while the metals which are below hydrogen cannot.
Zinc is above hydrogen, so it displaces hydrogen from hydrochloric acid to form zinc chloride and hydrogen gas.
Zn + 2HCl → ZnCl2 + H2↑
Copper is below hydrogen so it cannot displace it from hydrochloric acid.
Cu + HCl → No reaction