The principal quantum number, denoted as n, is one of the four quantum numbers which define the unique quantum state of an electron. The principal quantum number essentially determines the overall size and energy level of an atomic orbital. It is a positive integer ($n = 1, 2, 3, \ldots$) that indicates the shell to which an electron belongs in an atom. As n increases, the orbital becomes larger, meaning the electron is further from the nucleus and has higher energy.

Given the options:

Option A: size of the orbital - This option is correct. The principal quantum number directly affects the size of the orbital. A higher principal quantum number indicates a larger orbital.

Option B: spin angular momentum - This option is incorrect. The spin angular momentum is related to the spin quantum number ($s$), not the principal quantum number ($n$).

Option C: orbital angular momentum - This option is partially correct in the sense that the principal quantum number indirectly affects orbital angular momentum because it determines the possible values for the angular momentum quantum number (l), which directly affects orbital angular momentum. However, the principal quantum number itself does not directly specify orbital angular momentum.

Option D: orientation of the orbital in space - This option is incorrect. The orientation of the orbital in space is determined by the magnetic quantum number ($m_l$), not the principal quantum number ($n$).

Therefore, the correct answer is Option A: size of the orbital, as it most directly and accurately describes the role of the principal quantum number.