Home Sharing is a feature which allows users of iOS devices to access their iTunes library from anywhere within their house and stream the content to their iPhone, iPod, or iPad. But now it seems that Apple has decided to kill this feature. At least for the time being.
As it turns out, the change only affects music playback, since you can still share video to nearby iDevices. However, this could be a temporary bug, as the lack of Home Sharing is listed as a "known issue" in the iOS 8.4 release notes.
Thus, until this gets sorted out, only Apple TV users will be able to broadcast music that they own from their OS X system to other parts of their house. The reason for the removal of Home Sharing for music in iOS 8.4 could be related to the licensing agreements concerning Apple Music, but the acknowledgement of this problem as a bug could prove this wrong.
On the other hand, Apple Music’s family plan allows families of up to 6 to access Apple’s catalog of content for $14.99 per month. So if you're looking to opt for that, then you won't be needing Home Sharing anymore.