The Endless is another name given to the gods and dragons of the world of Breath of Fire IV. These Endless were not originally inhabitants of the world however, and have been summoned into it, most of the time by the mediums from the the village of Chek. Where they do come from is never properly explained, though it is assumed that arrived from the same world. A possible theory is that they were summoned from parallel worlds, the worlds of the previous games, which could explain the presence of Deis, who appears exactly as she was in her previous incarnation.
Not all these summonings however were performed correctly. The people of the Empire of the West attempted their own god summonings, but with a lesser result. Deis was summoned without a physical form, and therefore forced to reside in a suit of armour, Ershin. Another dragon meanwhile was ripped into two, his soul split into two parts. These 'parts' became Fou-Lu and Ryu, the former appearing centuries before the latter due to the summoning complications, and forced to wait until his other 'half' was born.
After Ryu joins with Fou-Lu in the 'good' ending, and has become whole, he decides that the Endless are no longer needed in the world, and that the people can now manage without them. He sends all the dragons, such as Pung Ryong and those who leant Ryu their powers, home. However, he decides himself to stay, and becomes mortal. Deis also decides that living in a suit of armour isn't so bad, and so she chooses to continue living in the world.
It would seem the gods are dead.
But we needn't worry about that...I can make as many gods as we want... or need.