What information is given by the magnetic quantum number

The magnetic quantum number distinguishes the orbitals available within a subshell, and is used to calculate the azimuthal component of the orbital that is specifies the orientation in space of an orbital of a given energy (n) and shape (l). This number divides the subshell into individual orbitals which hold the electrons; there are 2l+1 orbitals in each subshell of orbital in space. Electrons in a particular subshell (such as s, p, d, or f) are defined by values of ℓ (0, 1, 2, or 3).

It tells us us how many orbitals there are in a subshell and the possible orientations of these orbitals. Its value is dependent on the angular momentum quantum number, l.

the amount of orbital angular momentum that an electron has in respect to a particular axis of rotation.