When referencing Tanach it is normal to mention a chapter and a verse. The chapter divisions were invented by medieval Christians, but have been universally adopted by Jews as well, because no convenient textual divisions exist within Tanach itself. There are parshiyah breaks, but they are too closely spaced and irregular in frequency to be useful. Given that nowadays we don't memorize Tanach and cannot instantly place verses upon hearing them, adoption of the Christian system (or one like it) was probably inevitable.
Sefer Breishit is unique among books of Tanach in that it perhaps has no need for such a system. This is because Sefer Breishit itself contains 10 or 11 "chapter headers" which divide the book into that many sections. Each header consists of the phrase "These are the generations of..." followed by the name of the main character in that section.
The section headers are as follows: [After each header verse, in parentheses, I've summarize the content of the section]
0. In the beginning God made the heavens and the earth. (1:1)
(Six days of creation plus Shabbat. Doesn't mention "generations" - it's sort of a prelude, not a full chapter. It gives background for the rest of Sefer Breishit.)
1. These are the generations of the heavens and the earth in their creation. When Hashem God made earth and heavens... (2:4)
(Adam and Eve; Kayin and Hevel; Adam's son Shet)
2. This is the book of the generations of [man/Adam]. When God made man, in the image of God He made him... (5:1)
(Genealogy from Adam to Noach; mankind does evil)
3. These are the generations of Noach... (6:9)
4. And these are the generations of the sons of Noach... (10:1)
(Division of nations after flood)
5. These are the generations of Shem... (11:10)
(Genealogy from Shem to Avraham)
6. And these are the generations of Terach... (11:27)
(Story of Avraham and Lot. Ends with Avraham's death)
7. And these are the generations of Yishmael, Avraham's son... (25:12)
8. And these are the generations of Yitzchak, Avraham's son... (25:19)
(Story of Yitzchak. Ends with Yitzchak's death)
9. And these are the generations of Esav... (36:1,36:9)
10. These are the generations of Yaakov... (37:2)
(Yosef story; Yaakov's family goes to Egypt; end of Sefer Breishit)
We notice that Yishmael's "generations" come before Yitzchak's, and Esav's before Yaakov's. This is natural, because Yishmael and Esav were firstborns. But their sections are much shorter - basically just genealogies. In contrast, Yitzchak's and Yaakov's sections are much longer and include lots of interesting stories.
It's somewhat confusing that the stories involving a character do not always correspond to that character's "generations". For example, the first few stories about Yitzchak are in Avraham's (actually Terach's) generations, while the early Yaakov stories are in Yitzchak's generations. This makes it seem like the "Yitzchak section" is actually more about Yaakov. And indeed, Yaakov attracts more of our attention in this section - but still, these stories are within the framework of Yitzchak's life story, until Yitzchak dies. After that point, there are more Yaakov stories, but since Yitzchak is gone, they are now within the framework of Yaakov's own section.
(When I said "after Yitzchak dies", by "after" I meant in terms of the storyline, not chronologically. Sefer Breishit is NOT exactly chronological. Specifically: the deaths of Terach, Avraham, and Yitzchak are recorded immediately after the last story which involves them. This is the case even though these people were still alive later on, when their kids take part in additional stories which don't involve them.)
We also notice that virtually every important male character in Sefer Breishit has a section devoted to him. The exceptions are Yosef (who is within Yaakov's section) and, more surprisingly, Avraham (who is within Terach's section). Wouldn't it have been more natural to name the section after Avraham, not Terach?
I think the answer is that Avraham's story is interwoven with that of Lot. Avraham and Lot are both descended from Terach. The end of Lot's story is when he escapes Sedom and has children with his daughters - who turn out to be the ancestors of the peoples Ammon and Moav. These peoples will go on to live in the "expanded" land of Israel just like Yishmael, Esav, and Yaakov's descendants. Thus they are all part of the same original Divine promise, which apparently was not just to Avraham, but to all the descendants of Terach. Later on, among Terach's descendants, Yishmael/Yitzchak and Esav/Yaakov receive separate sections. But because Lot's genealogy is so brief (19:37-38), and because his entire life story involves Avraham, Avraham and Lot end up appearing in the same section, which overall is named for their common ancestor Terach.