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.
