Emanation in Eastern Orthodox Christianity is the idea that everything in the world, including human beings, come from God. It's like if you were a toy and your mom made you, you would come from your mom. But God didn't just create everything like a toy factory, God put a little bit of himself into everything he created. So everything in the world, including people like you and me, have a special part of God in them.
The idea of emanation is important in Eastern Orthodox Christianity because it helps people understand that everything is connected to God. It's like God is the sun and everything else is like a ray of sunshine that comes from the sun. So even though we are all different and have our own personalities, we are still connected to God in a special way.
Emanation also helps people understand that everything in the world is important, and that everything has a purpose because it is a part of God. So even things that seem small or unimportant are actually very special because they come from God.
In summary, emanation in Eastern Orthodox Christianity is the idea that everything in the world, including people, come from God and have a special part of God in them. It helps people understand that everything is connected and important because it comes from God.