It tells the character's background story as an overhead of what is to come in the future. In particular, the episodes dedicated to characters other than Noctis always come back to showing their connection with Noctis. The four characters have an episode of their own and each episode also shows their connections with each other. This is really important as if we are going to be experiencing this game we would love to know more about these characters and who they are. A prequel of sorts that tells the story from a more character-based perspective. I find it to really deliver on that aspect.
It's there to present the fans of the series who have been long anticipating this game to connect with the characters and build on them. While I would like a full blown 25+ episode anime made for this game, I can see why this exists and its purpose.
Now I have waited a decade for this beautiful game so seeing an animation short is pretty sweet. Brotherhood: Final Fantasy XV is a five episode short(special sixth episode limited to the special editions) that is supposed to be a treat for those like me who are anticipating the grand game.