http://static.zenimax.com/bethblog/oldcontent/morrowind_logo.jpg

http://nightmaremode.net/wp-content/uploads/2011/07/the-elder-scrolls-5-skyrim-logo.jpg

Is it even the dragonborn logo? Is it the Akatosh logo? What is it? Never heard it named in-game.

It's an imperial symbol, specifically. Makes enough sense for Skyrim, especially with the bit chipped away. The empire's fate is at stake. The Empire however isn't the most important part of Morrowind. Not sure why the diamond dragon symbol is prominent.

Ok, that clears up a lot.

The Empire sent the Nerevarine. Basically the empire symbol combined with the Almsivi daedric script symbolizes the main quest pretty well.

Aquilinius:

The symbol has its origins as a combination of two symbols: the Red Diamond and the Dragon.

The Red Diamond symbol has mythic significance stretching back to the formation of the Empire, when Alessia obtained the Chim-el Adebal (the Amulet of Kings) from the Ayleids. It also has important significance in that it resembled the hole in Pelinal Whitestake's chest - a representation of Shezzar's missing heart.

The Dragon symbology came with the Akaviri and was incorporated into the Red Diamond into the form we see it today. Since it came from the Akaviri dragon hunters, it is notably a symbol of the dragonborn.

I'm not 100% sure of all this, but I'm too lazy to go citing sources right now. Maybe someone else will.