So pretty much in FFXV there is a giant crystal that wields energy, which materializes in incredibly powerful magic. Only those of royal blood can use the full magic of the crystal, which is manifested in a lot of offensive and defensive magic (the super specifics haven't been discussed yet as that's likely to be answered in the game). In royalty's case, they also get access to summons. Now, for the Kingsglaive, they get granted power in a powerful manner, but not quite as sophisticated or complex.

We do get to see how the magic is transferred from royal to royal through a ring. This ring channels the magic of the crystal, along with the acceptance of these god-like beings known as the Old Kings or the Archaeans. If you're deemed worthy by the Old Kings, you can use the magic of the crystal without limits. In the movie, we get to see essentially judgment being passed by the Old Kings. If you're worthy to get the direct magic, you're in. If you're unworthy, you're pretty much set on fire. From the king, it leads me to believe that he can spread out the magic however he sees fit. In this case, the magic was passed along to the Kingsglaive, who are basically a sort of spec ops/black ops military faction who are in charge of protecting the king and the royal family.

A lot to explain but hopefully it makes sense? If it helps, here's a wikia, just jump down to setting: http://finalfantasy.wikia.com/wiki/Final_Fantasy_XV and the full plot for Kingsglaive: http://finalfantasy.wikia.com/wiki/Kingsglaive:_Final_Fantasy_XV