The Torah (Shemot 12:13) teaches, in the context of the commandment to don tefillin, "And it shall be to you as a sign upon your hand and as a remembrance between your eyes, in order that the law of the Lord shall be in your mouth."
The gemara (Shabbat 108a) derives from this verse that the parchment, upon which the sofer writes the parshiot, must be produced from a species which is "mutar beficha" (permitted to eat). Therefore, one must use the hides of a kosher animal (behema tehora or haya tehora) or a kosher bird (of tahor). The gemara refers to the species of the animal; however, the animal does not need to be ritually slaughtered (shehita). Also, one may not use the skin of a kosher fish.
Are certain parchments preferred over others? Interestingly, some of the Posekim (see Rama MiPano 37, as well as the Kaf HaHaim) write that it is preferable to write on the skin of an unborn calf (an embryo taken from its mother after being slaughtered), known as ‘or shalil’. This skin is soft and easy to write on. Also, some add that the skin of the young calf is preferred as it has not benefitted from, nor sinned in this world.
The Aharonim also question whether other sefarim (books of the Tanach) may be written on the hides of non-kosher animals? Some (see Beur Halacha 32:12) write that ‘the names of God which may not be erased’ must be written on parchment made from a kosher animal. If the names, however, are only abbreviated, or alluded to, such as a ‘dalet’, then they may be written even on the hides of non-kosher species.