The Yerushalmi (Pesachim 10:1) prohibits eating matzah on "Erev Pesach." The Rishonim debate when this prohibition begins: Baal Hamaor (15b) says it's from the time chametz can no longer be eaten, the 6th hour into the day. Ramban (Milchemes 15b) learns it's the whole day since one is obligated in Biur Chametz from the night before (how most understand the Ramban, unlike the Orchos Chaim 114).
L'Halacha, the Magen Avraham (471:6), rules the night before. Rama (471:2) and many other poskim (Magid Mishnah, Levush, Elyah Rabbah, Graz, Mishnah Berura, etc.) rule like the Ramban that the only prohibition is on the day of Erev Pesach, not the night before.
The rule that one is permitted to eat matzah the night before pesach refers to the rabbinic prohibition, as described by the Rambam (6:12).
However, the Shiyarei Knesses Hagedolah (B.Y. 473:3) says many are accustomed to refraining from eating matzah from Rosh Chodesh Nissan. Mishnah Berura (471:12) mentions this custom.
R' Moshe Feinstein (O.C.1:155) mentions that some even have the custom of refraining from matzah from 30 days prior, starting on Purim. In the response, he explains this custom, along with each previous one, saying that each has a basis in halacha. He ends at a minimum one should be stringent like the Magen Avraham and not eat matzah from the night before pesach.