A triangle fan is a way to draw a bunch of triangles together in a shape. Imagine you have a bunch of triangles that you want to draw, but you want to make them all look like they are part of a bigger shape, like a circle or a square. To do this, you can arrange the triangles so that they all share a point in the middle, like the spokes of a wheel. This point in the middle is the center of the fan.
When you draw the fan, you start at the center point and draw one triangle. Then, you move around the circle a little bit and draw another triangle that shares one edge with the first triangle. You keep doing this, moving around the circle and drawing triangles that share edges with the ones you've already drawn. Eventually, you will have drawn all the triangles and you will end up back at the beginning.
This is called a "fan" because the triangles all radiate out from the center, like a bunch of leaves on a stem. When you're done drawing the fan, you'll have a bunch of triangles all connected to each other, making a bigger shape.
Triangle fans are often used to create 3D shapes on a computer, like a 3D model of a house or a car. By drawing lots of triangles in a fan shape, you can create a complex 3D object that looks smooth and realistic.