Double replacements are not reversible because a pair of the ions is removed from the solution.
BY FORMING A PRECIPITATE
AgNO₃ + KCl → AgCl + KNO₃
The ionic equation is
Ag⁺(aq) + NO₃⁻(aq) + K⁺(aq) + Cl⁻(aq) → AgCl(s) + K⁺(aq) + NO₃⁻(aq)
Since silver chloride is insoluble in water, the Ag⁺ and Cl⁻ ions take each other out of the solution and become unavailable for the reverse reaction.
BY FORMING A GAS
Na₂S + 2HCl → H₂S + 2NaCl
The ionic equation is:
2Na⁺(aq) + S²⁻(aq) + 2H⁺(aq) + 2Cl⁻(aq) → H₂S(g) + 2Na⁺(aq) + 2Cl⁻(aq)
The H⁺ and S²⁻ ions form H₂S gas, which escapes into the atmosphere, so it cannot participate in the reverse reaction.
BY FORMING A NONELECTROLYTE
HCl(aq) + NaOH(aq) →HOH(l) + NaCl(aq) or
H⁺(aq) + Cl⁻(aq) + Na⁺(aq) + OH⁻(aq) → HOH(l) + Na⁺(aq) + Cl⁻(aq)
The H⁺ and the OH⁻ ions react to form water, which is a nonelectrolyte (does not form many ions). The H⁺ and the OH⁻ ions are removed from the solution.
Simple explanation, nice font are on this site: http://firstlightastro.com/DOWNLOADS/RXNS_Ch9_DD.pdf