As per IUPAC gold book , reduction and oxidation are defined as follows$^1$$^2$.
A reduced species can be formed also through the gain of electrons (either at the negative electrode in a cell or through transfer from another atom, ion or group of atoms in a chemical reaction).
Oxidation consist in removal of one or several electrons from the substrate.
The above equation can be divided as oxidation half reaction and reduction half reaction.
- In the reduction half , Silver in $+1$ oxidation state gains $2$ electrons to form $\ce{Ag}$. This is reduction.
$$\ce{2Ag^+(aq) -> 2 Ag(S}$$
- In the oxidation half , Copper in $0$ oxidation state looses $2$ electrons to form $\ce{Cu^2+}$.
$$\ce{Cu(S) -> Cu^2+(aq)}$$
In , organic chemistry , Ethyne conversion to Ethene is reduction. Further Ethene conversion to Ethane is also reduction.
Further , the following series are also taken to be reduction and oxidation (in organic chemistry).
References
$^1$ IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). Online version (2019-) created by S. J. Chalk. ISBN 0-9678550-9-8. https://doi.org/10.1351/goldbook.
$^2$ IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). Online version (2019-) created by S. J. Chalk. ISBN 0-9678550-9-8. https://doi.org/10.1351/goldbook.