Does the iAd App Network shutdown mean my app will no longer display ads?
Yes, you need to move to a different provider.  With iAds shutting down, and assuming you don't have any other third-party provider, such as AdMob, serving you ads, your app will not display any ads after the shutdown on June 30.

The iAd shutdown was announced almost a year ago, giving developers ample time to find other providers and other ways to serve ads.