The word bereshit (בְּרֵאשִׁית) can mean "in the beginning" or "at the start" or "at the head of (all things)," etc. (notice the term rosh (ראשׁ, "head") appears embedded in the word as its shoresh (root)). In Jewish tradition, the word can refer to either the first weekly Torah portion (parashah) in the annual Jewish cycle of Torah reading (called "parashat Bereshit") or to the first book of the Torah itself (called "Sefer Bereshit"). When used to refer to the first book of the Torah, bereshit is sometimes called sefer rishon (the First Book) or sefer beri'at ha'olam (the Book of the Creation of the world). The ancient Greek translation of the Torah (i.e., the Septuagint) called the book "Genesis" (Γένεσις: "birth", "origin") instead of using the translation of the first Hebrew word (בְּרֵאשִׁית), i.e., ἐν ἀρχῇ, for the book's title. The translated term "Genesis" was used in subsequent Latin and English translations of the book.
As a bit of textual trivia, if you connect the last word of each book of the Torah can tell the story of the entire Torah... Genesis ends with the word be'mitzraim (בְּמִצְרָיִם), "in Egypt"; Exodus ends with ma'sehem (מַסְעֵיהֶם), "their journeys"; Leviticus ends with "Sina"i (סִינָי); Numbers ends with "Jericho" (יְרֵחוֹ), and Deuteronomy ends with "Israel" (יִשְׂרָאֵל). If you string these words together you get something like, "The people were in Egypt, but they journeyed, first to Sinai, then to Jericho, and finally into the land of Israel."