Apple IDs are basically accounts you create to buy things from Apple. They are also used to sign in and use for services like Find My Friends, iMessage (and Messages), and other mostly iCloud-related services like syncing contacts and calendars.
There have always been problems with Apple IDs. You end up with more than one of them, and some of your purchases are in one, some in the other(s). In most cases it is difficult or impossible to use more than one at a time, so many purchases are abandoned and bought again in the "correct" Apple ID. Another big issue is when a family decides to use one Apple ID to share purchases among family members. There are workarounds for this, but what happens when the kids grow up and want their own accounts? They then lose access to everything that was purchased by the family, including those that were specifically bought for them.
A related issue is curating and controlling what children purchase. Children under 13 could not have an Apple ID. Parents could choose to create an ID with fake age information and then either control the password, give the child access to anything they wanted, or use iTunes gift cards. Or they would use the parent's ID, and be given the password (or not).
It was a big mess and nobody liked it. For years we have all been begging Apple to allow us to merge all our IDs and solve the issues with children and other family members. They finally have.
Apple calls it Family Sharing. Up to six people can share purchases from iTunes, iBooks, and the App Store without sharing accounts. All purchases are paid for by the account that sets up Family Sharing, with the same credit card. Anyone can be designated as a "child," which results in any of their purchases requiring approval. Photos and calendars can be shared. Anything a family member owns can be hidden from others. Location sharing can be turned on or off.
Family Sharing requires iOS 8 and Mac OS X 10.10 (Yosemite). As of this date, iOS 8 has been released but Yosemite hasn't. Family Sharing will work on iOS devices but not on Macs yet. So in most cases, you will want to avoid it until you have both Yosemite and iOS 8 on all devices used by "family members." Every Mac and all but the newest iOS devices will have to be upgraded, and some will not qualify for the upgrades.
Its a solution limited to "families" with a lot of shiny new, or almost-new devices. But it seems to be an elegant one. Thank you Apple.