I would like to add some information to Camps's answer. In essence, the band structure should consider the information about each quantum state obtained by solving the Kohn-Sham equation for the periodic solids. The quantum state for solids can be formally expressed as:
$$|atom, k, orbital,spin\rangle$$
The band-gap can be considered as global information extracted from the whole band structure while the effective mass can be considered as the deduced information from the local part of the whole band structure.
As the state indicated, you can obtain more information from the projected band structure. [If you use VASP, all related information is printed in the PROCAR file.] Therefore, you can know that each state in the band structure is contributed by atom, orbital, and spin. I will give you some examples:
- Project to the atom (PtSe$_2$/MoSe$_2$):
- Projected to the orbital (PtSe$_2$/MoSe$_2$):
- Projected to the spin (MoS$_2$):
Ref:Tunable giant Rashba-type spin splitting in PtSe2/MoSe2 heterostructure
As for the density of states, the $k$ information in each quantum state is integrated.
What information can be obtained is like the band structure.