It's significant for a number of reasons.
First, it sets the backdrop to a romantic comedy which is concerned with the relationships between men and women. At the start of the play, the men have been absent at war. Now they are returning, victorious, and the thoughts of both men and women turn from war to love. Thus Claudio rapidly abandons his soldierly self and falls in love with Hero. Benedick and Beatrice are able to resume the 'merry war' that has always been part of their meetings in the past.
Second, the war gives a motive for Don John's hatred and jealousy of his half-brother, Don Pedro, and of Claudio. Don John, being illegitimate, could never achieve the status or power of Don Pedro, and used the war as a pretext for staging a rebellion against him. He failed, and the two were reconciled - though Don John is merely biding his time to make trouble.
Third, war is used in the play as a way of reflecting on relationships. Benedick is disgusted by the way that Claudio loses his masculinity, as he sees it, by losing interest in soldierly things ('a good armour', 'the drum and the fife'), and becoming a lover. The fact that Benedick is so convinced that this will never happen to him of course makes it all the more funny and delicious when it does!
Finally, Don Pedro offers to help Claudio win Hero's hand in marriage by undertaking what's called a 'proxy wooing' - that is, he courts Hero in Claudio's name. In setting up his plan, Shakespeare has Don Pedro speak in noticeably military terms: he will 'take her hearing prisoner with the force/ And strong encounter of my amorous tale.'