Atomic orbitals are regions around an atom's nucleus where electrons are most likely to be found. They are described by a set of quantum numbers: the principal quantum number (n), the azimuthal quantum number (l), the magnetic quantum number (ml), and the spin quantum number (ms).

The principal quantum number (n) indicates the energy level of the orbital. For example, the first energy level (n = 1) contains only an s orbital, while the second energy level (n = 2) contains s and p orbitals. As the value of n increases, the energy and the size of the orbital also increase.

The azimuthal quantum number (l) determines the shape of the orbital. It can have values ranging from 0 to (n-1). For example, an l value of 0 corresponds to an s orbital, an l value of 1 corresponds to a p orbital, and so on. The letter designations s, p, d, and f are derived from spectroscopic notation.

The magnetic quantum number (ml) specifies the orientation of the orbital in three-dimensional space. It can take on integer values ranging from -l to +l. For instance, a p orbital has three possible orientations: ml = -1, 0, or +1. Each orientation is represented by an individual p orbital.

The spin quantum number (ms) describes the spin of the electron within the orbital. It can have two values: +1/2 (spin up) and -1/2 (spin down). According to the Pauli exclusion principle, no two electrons can have the same set of quantum numbers, which means that a single orbital can hold a maximum of two electrons with opposite spins.

In summary, atomic orbitals are characterized by quantum numbers, which provide information about the energy, shape, orientation, and spin of electrons. Understanding these concepts is crucial for interpreting the behavior and properties of atoms.