About Face and Vertex Normals
Basically a mesh is made of collection of polygons (triangles, quadrangles, n-gons...), delimited by edges and vertices.
A closed polygon defines a face, which can be facing in one direction or the other. The face normal defines its direction.
A closed polygon has vertices at each corner, and each vertex has its own normal. The vertex normal defines how virtual light will bounce off the mesh, defining a smoothing for the underlying mesh.
The normals of the vertices are attributes of the mesh.
Additionally to normals, a mesh can have other attributes like UVs, tangents, binormals, etc... that define how it will behave when rendered in a 3D application.
Please have a look the following pages to learn more about meshes and meshes attributes