The word “Torah” is a tricky one, because it can mean different things in different contexts. In its most limited sense, “Torah” refers to the Five Books of Moses: Genesis, Exodus, Leviticus, Numbers, and Deuteronomy. But the word “torah” can also be used to refer to the entire Hebrew Bible (the body of scripture known to non-Jews as the Old Testament and to Jews as the Tanakh or Written Torah), or in its broadest sense, to the whole body of Jewish law and teachings.
Each week in synagogue, we read (or, more accurately, chant, because it is sung) a passage from the Torah. This passage is referred to as a parashah. The first parashah, for example, is Parashat Bereishit, which covers from the beginning of Genesis to the story of Noah. There are 54 parashahs (parashiyot), one for each week of a leap year, so that in the course of a year, we read the entire Torah (Genesis to Deuteronomy) in our services. During non-leap years, there are 50 weeks, so some of the shorter portions are doubled up. We reach the last portion of the Torah around a holiday called Simchat Torah (Rejoicing in the Law), which occurs in September or October, a few weeks after Rosh Hashanah (Jewish New Year). On Simchat Torah, we read the last portion of the Torah, and proceed immediately to the first paragraph of Genesis, showing that the Torah is a circle, and never ends.
The Torah and haftarah readings are performed with great ceremony: the Torah is paraded around the room before it is brought to rest on the bimah (podium). The reading is divided up into portions, and various members of the congregation have the honor of reciting blessings over a portion of the reading and doing the reading. This honor is referred to as an “aliyah” (literally, ascension).