Religion in Game of Thrones
Azor Ahai Prophecy
The Original Long Night
A popular understanding of a human-like God in the Game of Thrones universe is when considering the Azor Ahai prophecy. The name of this prophecy is in regards to the person who saved the earth during the last long night. The long night, also known as the war for the dawn was an apocalyptic takeover of the world by undead creatures known as "white walkers".
This takeover caused the longest Winter that has ever happened, causing many crops to run dry, and many people to starve. This war lasted a generation long, and was nearly impossible to beat due to the fact that any people killed by the creatures would regenerate as part of the dead. The end never would have come if it was not for Azor Ahai.
Azor Ahai wielded a sword named "light bringer" from the faith of the Lord of Light and was able to bring light back to the world, and for peace to come again. This figure is extremely legendary in regards to religious figures in Game of Thrones. This is the person who saved the world.
Prophecy as God Wielding
In current time of the Game of Thrones story, there is a need for a modern Azor Ahai figure as the War For the Dawn is beginning once again and the White Walkers have began pushing beyond the wall.
The prophecy refers to someone beating the war once again in a similar way that Azor Ahai once did. The prophecy does not state that this person will be exactly this, but there will need to be someone who will take the place of the last person who saved the world from darkness. This person is a God-like figure to those who believe the war is coming - and especially to those who praise the Lord of Light. Melesandre, the red priestess, understands that beating the war is a nearly impossible task, therefore, she searches for who this person will be. When Jon Snow comes back to life she believes he must be "The Prince Who Was Promised", also known as Azor Ahai.
Requirements of the Prophecy
A prophecy acts as a subset of factors that must fit an individual in order for them to achieve the desired act. Not just anyone can fulfil a prophecy, and in this case: save the world. There are requirements for this type of theory to come true, but the nature of a prophecy is very vague. Therefore, these requirements may not be applied in an obvious sense, nor will they seem important to the overall endgame.
The Azor Ahai prophecy (from multiple sources) states:
They must have been born under a bleeding star, amongst smoke and salt
They must wield a burning or flaming sword named "light bringer"
They will likely sacrifice the person they love or are married to
They have something to do with dragons
They have Targaryen blood
"The dragon has three heads", likely meaning there are three important people involved
"Who is Azor Ahai?"
By Alt Shift X
This video gives background and history regarding the prophecy, as well as providing theory as to who it could be in the modern series.
Who Fits?
Although it is never outright revealed who Azor Ahai is in the television series, it seems as though it ends up being a combination of people (as stated in the prophecy).
By definition of the prophecy, and once it is revealed Jon Snow is actually born of Targaryen blood: him and Daenerys are both equal contenders. This makes sense of their powerful influences as they must have survived The War of the Dawn to be able to be crucial members in ending it. They are both untouchable figures in the series, and I would suggest it is due to their God-like influence that is naturally embedded in them. If this prophecy is true, then both of them have a naturally higher power that must be used for good.
Although at the end of the series, it is neither of them that kills the Night King, effectively ending the War For the Dawn, it is Arya Stark, they both aided in fighting the war in a crucial way. I would claim the three-headed dragon from the prophecy refers to Jon, Daenerys, and Arya.