Niharika

FULLERENE is an allotrope of Carbon having closed three-dimensional structure like a ball. We usually call it a Buckminster ball too. In other structures of Carbon, i.e. Graphite, here we have a 2D bonds between carbon(3 per atom) and electrons in between the layers are free. We don't see any binding between 2 parallel layers, and in Diamond, we have a 3D bonds placed as a tetrahedral shape with connections with all four other carbon atoms. In fullerene also we have three bonds per carbon atom, but the geometry of arrangements have no surface loose ends. It is generally explained using pentagons and hexagons. We learn about fullerene as they have unique properties which lead to the synthesis of Carbon nanotubes.
I hope that I have explained this little bit. I have no idea about the level of your education and have answered this question, keeping in mind a class 10-11 child.