What information is given by the magnetic quantum number

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

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.