We have seen the World of Warcraft logo change from expansion to expansion, but we can always count with the theme of the expansion to somewhat affect or influence the design or colors of the logo.
An example of this is the Wrath of the Lich King logo had the icy-frosty elements around the frame. It represented the chilly lands of Icecrown.
The Cataclysm logo had the deep black and fiery shattering highlights representing the breaking of the world, and earthquakes caused by Deathwing.
Mists of Pandaria had a jade-like green background with old-school Warcraft III yellow-orange text for Mists of Pandaria. Chen. Jade serpent. Warcraft III. Got it.
Warlords of Draenor had the wood and iron motifs, representing the Iron Horde. The map of the world within the logo is the known continent of Draenor.
LEGION logo with heavy green shades with black text represent the fel of the Burning Legion.
Now we are landing on Battle for Azeroth with a deep blue background, and some golden highlights around the text and frame.
The answer is quite easy and straightforward here. The sword of Sargeras scars the land of Silithus. The worldsoul of Azeroth is deeply wounded, and it is bleeding out its lifeblood everywhere around the world. The logo motif represents the wounded world of Azeroth, bleeding out Azerite — which the developers described during the World of Warcraft: Gameplay & Systems panel:
The assault from the Legion has grievously wounded our planet, and cracks are occurring all across her surface. She is hemorrhaging her life-blood, and it looks like this sort of gold-blue substance that you see behind me. As it emerges, it crystallizes into these thrumming Spires filled with power that reach towards the sky.
There is incredible power inherent with the blood of Azeroth, which we are calling Azerite. But for the Alliance and the Horde, this is a little bit like being the first group to discover plutonium. While incredibly powerful, we are not entirely sure what all it can do, and some of those mysteries you will be exploring in Battle for Azeroth.