Which element is undergoing reduction in the following reaction: Zn(s) + 2 AgNO3(aq) → Zn(NO3)2(aq) + 2 Ag(s)?

The silver ion, ##Ag^+##, is reduced to silver metal, ##Ag^0(s)##.

The silver species formally undergoes a decrease in oxidation state from ##+I## to ##0##. For every reduction, there is a corresponding oxidation, and zinc metal is oxidized to ##Zn^(2+)##.

##Zn(s)uarr + 2AgNO_3(aq) rarr Zn(NO_3)_2(aq) + 2Ag(s)darr##

In other words, reduction is gain of electrons, whereas oxidation is loss of electrons (LEO says GER, loss of electrons = oxidation; gain in electrons = reduction). You will have to remember this.