Create data structure associated to a mesh

Hi! I need some help with an exercise. I'm not asking for solutions but only an explanation of what I am supposed to do, because this is the very first time I have to do this. I'm asked to create a data structure associated to some mesh, which can be used to realize operations as computing/returning the number of triangles in the mesh, the number of degrees of freedom, etc.

My problem is that I'm a bit confused. A few weeks ago, when we generated meshes with Gmsh, the .msh file had information about the entities, the nodes, etc. and for me it already is the structure of a mesh. Can someone explain to me what I should do, maybe with some other words, please?

If needed, I attached my exercise sheet.