The term sidra originally meant ‘order’ or ‘arrangement’ (seder) and is frequently used in the Talmud to denote a section of the Bible either read in the synagogue or studied in the study hall. In the Gemara (Yoma 87a) Rashi explains the statement that Rav read a sidra before Rabbi (Judah the Prince) to mean a section of the Prophets or the Hagiographa.
The Talmud Yerushalmi (Ta’anit 4:3) applies the term sidra to a section of the Torah to be read in the synagogue. In the Gemara (Shabbat 116b) it is said that in Nehardea the people used to read a sidra of the Hagiographa at the Mincha service of Shabbat. Tosafot (ibid. 24a), however, explain this to refer to the Haftara, which they used to read at the Mincha service. The word sidra also appears in Megilla (21). Later this term began to be used by the Ashkenazim to denote the weekly portion of the Pentateuch, just as parasha is used by the Sepharadim.
Masechet Sofrim, one of the minor tractates (end of chapter 16), explains that there were 175 sedarim or parashiyot, one for each of the years our Patriarch Abraham lived. Nachalat Yaakov (ibid.) explains that the reason for so many sedarim is that in those years they would complete reading the Torah in Israel in 175 weeks, or three-and-a-half years, 50 sedarim (or sedarot, the Hebrew plural - and its possessive form, sidrot) in one year. In Babylonia and at the present time, the Pentateuch is completed every year (baraita, Megilla 31a).
The Masorah figures the sedarim (sedres in Yiddish) at 158, which is the number you will find itemized at the end of the Five Books of Moses. This assumes that the Pentateuch was completed in approximately three years, not three-and-a-half years.
Today, when we complete reading the Torah in one year, we figure the number of sedarot/sedarim at 54. The Masoretic Bible published by Ginsburg (London 1894) lists the division of the sedarim/sedarot according to the triennial cycle. The Jewish Encyclopedia (1905) also lists that number.
The Gemara (Megilla 31) itemizes the order of the weekly and festival readings according to the many divisions which Ezra the Scribe and his Anshei Knesset HaGedola (the Men of the Great Assembly) established as well as the reasons for it. According to Rav Achai Gaon, the sections were combined to be read in one year during the era of the Amoraim in Babylon. The annual cycle, in which we repeat the Torah every year, was established because of the persecution of Jews that started at that time in the Diaspora, and it was difficult for Jews to study the Torah. In order not to forget the Torah, they condensed the cycle from three years to one year.