There are a few things this does for Ezreal. First, it converts his Q damage into magic damage. That allows it to work against his opponents MR (tends to be lower than armor), and allows it to benefit from his magic penetration. Those are both major increases to his potential damage. Lichbane doesn't do that. You actually end up with more damage on a runeglaive Q than a Lichbane Q just because of this one trait. Seriously, it hurts more than Lichbane does just because you can use your magic penetration.
However, that's not the only damage benefit. Runeglaive allows your autoattacks to proc spell effects, which for Ezreal means that his Q can proc spell effects. This makes Luden's Echo wonderful for AP Ezreal. Normally, Ezreal's Q won't proc Luden's, but it will if you have Runeglaive. That's a lot of extra poke than any other kind of Ezreal just doesn't have access too.
Additionally, the mana sustain does exist in lane for AP Ezreal. Go mid, Q the chickens over the wall, get mana back. You can stay at around 25% mana forever even you farm entirely with Q. No one can deny you any farm, and you turn into an annoying spamming poker that is very, very hard to bully, pressure, or kill.
This is also where the AoE comes in. Traditionally, one of Ezreal's weaknesses is that he can easily be pushed in. He has no form of waveclear outside his ultimate, so shoving it in and forcing him to farm under tower is a great way to lower his farm and make him generally miserable. With Runeglaive, he has enough pushing power on his Q to prevent attempts to force him in.