We are not actually told a whole lot in the play about the war Don Pedro has just returned from. We do, however, know two things: 1) Historically, this play is set during the time of the Italian Wars, which spanned from 1494 all the way until 1559, only five years before Shakespeare was born in 1564; 2) Don Pedro's illegitimate brother Don John attempted to overthrow Don Pedro's reign, but they were "reconciled."
We see Don John's reconciliation to Don Pedro mentioned in the first scene when Don John is first introduced to Leonato. As Governor of Messina, Leonato welcomes Don John into his home as a trustworthy member of the city due to reconciliation, saying, "Let me bid you welcome, my lord. Being reconciled to the prince your brother, I owe you all duty" (I.i.132-133). However, it has been pointed out that both logically and historically it does not make a great deal of sense for Don John to still be alive had he just conducted a major coup. Elizabethans would know from their own history that the only way to deal with one who tries to overthrow the monarchy is to try him for treason and have him beheaded ("The Artificiality of Messinian Society," eNotes). Hence, because Don John has been "reconciled" to Don Pedro, we may be able to assume that it was not a major coup, just a small skirmish, and, therefore, the war they are returning from was not of Don John's initiation.
Hence, we are left to speculate that the war they have returned from refers to one of the Italian wars although we don't really know which one. We do know that Don Pedro is Prince of Arrogan of Spain and as Prince of Arrogon he would also rule over Sicily, which included Messina (Delahoyde, "Much Ado About Nothing"). There were many victories over France all throughout the history of the wars; however, several battles led to victory over France culminating in complete Spanish supremacy in Italy and Spanish ownership of both the Sicilies, which would include Messina and Milan. These battles spanned from 1556 to 1559. The play could be referring to any one of these victorious battles, including the final victory.