In the ancient world, genealogies were important to justify the divine right that royalty claimed, and the divine ordination that priests claimed. In Judaism, besides those two (which were very important in Israel along with the ancient cultures), genealogies were important for land ownership. In ancient Israel, only Israelites were able to use land, and they had each gotten their allotment to be with their family in perpetuity. Therefore genealogies were important for the perpetuation of the family with regard to property and therefore income.
In addition, the genealogies of the Bible serve to show that it's a historical record and not a fictitious one (though we're all aware that genealogies can be fiction, as in Lord of the Rings). There was no such notion or reality in the ancient world, however. Genealogies were historical; there is no record of a fictitious genealogy. Computers are now able to do broad studies of names (onomastic studies comparing biblical names with what has been found on artifacts and documents), and the few that have been done verify the accuracy of the biblical text.
These is no reason to try to memorize or learn most of these names or places, however. Most of the people never show up again, and some of the places don't. If you need to find them again, you can just use a word search.
> How important are those locations?
Scholars want to know where they are, of course. If they are legitimate sites, it lends credibility (but doesn't prove it) to the account. If all the names are made up, it leans us toward fiction.
In Genesis 14, for instance, these places are all legit. They are actual place names, and archaeology has confirmed that they existed during Abram's era. Even some of the names have corroboration. It makes us lean towards Gen. 14 being a historical account, like so much else in the Bible.
Genesis 14.1
- Amraphel is a Semitic name, but is an unknown person. Names with a-ph-el are common.
- Shinar is in southern Mesopotamia, which at the time was characterized by independent city-states.
- Arioch is a Hurrian name. It is linguistically the same are Arriwuk, the name of a vassal of Zimri-lim, a contemporary of Hammurabi. The name disappears after the middle of the 2nd millennium.
- Ellasar is an old name for Assyria. A city names Ilan-sure is known from Mari archives.
- Kedorlaomer is a name that follows the pattern of Elamite names.
- Elam is the region east of Mesopotamia—present day Iran.
- Tidal. There are at least 5 Hittite kings with this name.
- Goiim means "nations," possibly meant as "barbarians." It is probably in eastern present-day Turkey.
All of this gives quite a bit of historicity and credibility to the text. The author wasn't making stuff up. In addition, the place names of vv. 5-7 are all identifiable. The political situation matches with archaeological records. The invasion could only have happened during Mesopotamia's Isin Larsa period: a 275-yr period after the fall of the Ur III culture when local city state rules struggled for power. Therefore we can place this event anywhere roughly from 2060 BC to 1949 BC.
That's what these names and places do, but there's no reason for you to learn them, try to remember them, or keep track of them.
> And is it important to know where those exact places are (geographically) to follow the story?
If you really want to follow the story, yeah, but if you just want to get the idea that there is local skirmish going on and Abram & Lot got caught up in it, then that's all you need to know.